Firstly, your post would be a lot easier to read if it was in paragraphs. As it is it's hard to pick out the information.

I also suspect that as you say your SD looks and behaves a lot like her natural father, whom you dislike, she's already behind the eight ball as regards you liking her. And so what if she's a tomboy? You say it like it's a bad thing.

You need to get together with your wife, let her know your concerns and make a joint plan that you both will stick to. Consistency is the key.

You say your wife is "very easy going" with the children. So, would she agree with you that their behaviour needs work? If not, she is not going to put the effort in to fix it, since for her it doesn't need fixing.

Is she "easy going" because she can't be bothered enforcing the rules? You say she "tells them to go to bed a thousand times". Why does she not put them to bed (they're still rather young (especially the 5 year old) to just tell them "go to bed" IMO) and make it clear that there will be consequences if they get up (and follow through with that)? If this is her attitude to child raising she is as much the problem as the children.

If they take food you don't want them to take, don't buy it. Buy only what you want them to eat. Have regular mealtimes. Have consequences for poor behaviour.

Raising a child with ADD is work, as Ceph will tell you, that requires patience and consistency and firmness. It doesn't sound like any of those qualities are present in your home ATM.

As I said before, you need a plan. But, the children's mother needs to be in on the plan wholeheartedly. If she's only agreeing to get you onside, she won't be making any effort to follow through with it and you will only get more frustrated. What will you do if things don't change? Is this situation a deal breaker? Or are you also willing to let things slide because it's too hard to follow through?

The baby is asleep, so I'll go through bit by bit until I get tired or the baby wakes up.

"my stepdaughter has ADD, a really hard case,"
I came into my stepson's life when he was 8. He has very severe ADHD, ODD and may be bipolar; I think he may also have an auditory processing disorder. 8yos with ADD are tough, but I swear it gets better!

"y wife and I both get really impatient but I notice that my wife is very easy going with her"
ADD also requires ENDLESS patience. It's really difficult.
But one key is to pick your battles. If they're able to hold a pleasant conversation, but have to be hopping on one foot and holding a spatula to do it, well...

"the girl is pretty much of a big liar, fights with her little brother a lot, has some pretty rough games with her barbies and other toys,"
With lying and fighting, ADD kids don't have the foresight or hindsight to see the possible outcomes of their action. Their brains are absolutely hell-bent on instant gratification, and our job as their loving adults is to help them learn the skills of foresight and hindsight.

"never cleans or organizes her bedroom, she's a very dirty girl, barely eats and whatever she eats she takes stuff out of the food/plate, but she gets tons of toys from everyone and everyone believes in her lies and all"
Hygiene issues are probably best dealt with by mom... But, does she actually KNOW how to keep herself clean? My SS is 12 now and we're still telling him "Wash your hands. With soap. Sing Happy Birthday. Make sure you get your nails, between your fingers, and your wrists too, instead of just the fronts and backs!" When he was 9 and I had to talk to him about HOW to wipe his bum because he honestly didn't know how.

"and I consider her a tomboy and honestly everything she does pisses me off,"
Does being a tomboy matter?
I think I'll be grateful if my 1yo DD prefers trucks to high heels at age 8!

"and to make things worse, she looks eeeexactly like her dad, the guy is a complete ass*** and both are exactly the same, the guy also has ADD, and physically, both look very alike."
This one you just have to get over. She can't control who her dad is.

"I really try my best to get along with her, give her advises, etc, I just really try my best, but for she misbehaves terrible every single day, without exageration,"
If you're open to how change in your family can begin with YOU, I can give you about a million ideas, coping strategies, tips and tools. But, if you are really honest with yourself, are you ready to change? It's OK if you're not ready - it's human to resist change, and you can come back to this when you do feel ready.

"there's never been a day that she's behaved perfect, even at school, her school teachers can't stand her, so we took her to a psychologist and a child psychiatrist and she's on a med to make her just focus and be calmed,"
Back the truck up! Meds don't MAKE kids focus and be calm. Meds facilitate the KID's own ability to focus and be calm.
Honestly, my SS can be unpleasant to be around without his meds too. But it's HIM being pleasant with his meds, not his meds being pleasant. I know I sound totally pedantic about semantics here, but it honestly does matter - it's a mindshift about how you approach your family.

Can you start smaller for her? How about aiming for a good ten-minute drive to Grandma's house? Then a good supper? Then a good HOUR? Then a good afternoon?
The ADD child's brain can't handle the abstract concept of "being good" for the incredibly long period of "an entire day."
I'll elaborate if you're open.

"but when she's not medicated, noone can stand her, my wife although she's easy on her, can't stand her much but she doesn't know that I've grown to hate this girl."
There have been times where I've felt little to no LIKE for my SS. And there are times when loving him is hard. He can make me totally crazy. I sometimes feel like he's a disruption to my nice little nuclear family. I sometimes feel like he's being a jacka$$ to spite me. But he's a kid and he needs to be loved.
If I expect the worst, he will give the worst. It's a self-fulfilling prophecy.
So every day, I get up and choose to love my SS. It took me a long time to get back there though (we started off well, took a bad turn, and are good now).

"I feel terrible for that but I don't know what else to do, am I just hysteric? is it because I'm not the real dad?"
It IS harder to love a child that isn't yours. Honestly, I don't love SS in the same way I love DD. But your SD needs her own niche in your heart.
You're not hysteric or crazy or evil. You sound as if you're at your wits' end though and are pretty desperate.

"I pretty much took over this family since my wife used to have a crappy life with her ex and the level these kids are at right now was pretty much an upgrade,"
I'm glad you were able to help with the status of the family! That shows that there's hope!

"and I'm always a nice guy most of the time, but I telecommute and feel like resigning to it and going back to the office cause the kids never listen to me,"
Would it help? Would the issues still exist when you came home from the office? Would it be worse? Would it be a solution or just an escape?

"their mom, although tells them to listen to me, they barely do or only listen to me when it provides them some type of benefit, so if I tell them to pick up their clothes and take it to the laundry room, ask me back if they do. They never go to bed on time, even my wife tells them to go to bed a thousand times and never do, we send'em to bed from 8 pm and it's 11 pm and they are still around, it's pretty stressful,"
Well, that's the first issue! Coparents need to be on the same page. Mom needs to step up and say "Wait a minute! I'm the mom and my family will treat one another with respect." And then she needs to make the expectations 100% clear to the kids, and STICK with it.
If you and your wife are up to it, this forum can certainly help you. But it's a real commitment.

"even with the food, we buy tons of food for the whole month and they pretty much consume even my stuff, so they don't have the lunch their served but take everything behind our backs, cookies, cheese, juice, coca cola (I wish they tool a tomatoe instead, haha)"
We give my SS a container each week with his junk food in it. That's what he gets for the week. End of story. If he eats it all in 24 hours, well, tough cookies for the next six days. We made this clear to him and he's usually fairly able to abide by it.
Also, just don't buy what you don't want them to eat!

"so anyways, I don't have any kids of my own, I just took this torch and became their dad, the guy is not the best father figure either way and these kids got so used for what it seems, to their new way of life at a much better house, car ride and stuff, instead of what their real dad gives them, bus ride, guy lives with his mother, didn't even finish high school."
Please try not to say anything disparaging about their dad to them. It's great that you're trying to be a good dad to them, but they may feel torn. They may want to be kind to you, but feel like their betraying their dad who's down on his luck, KWIM?

Anyhow, if you're willing to make major changes, I'm willing to use my tiny scraps of free time to help you!

I'll add a possible about the food situation. Depending on meds and med schedule, some meds 'zap' the child's appetite. I had trouble getting my little one to eat lunch but usually got her to eat a healthy but decent sized breakfast before she took her meds for the day. Some children when the meds wear off will do a lot of compulsive eating. If the parent buys a large amount of junk, any child will tell you 'junk' taste better than 'icky' food LOL...get rid of the soda, all the bags of cookies blah blah. As Ceph said, as they get a bit older the tub idea does work. Your wife may have to actually go to the store more often instead of buying 'tons' at a time for now. She may for now also actually have to keep tempting items in a locked closet for similar type solution to food sneaking.

Consistancy is all important and a lot of supervision during requested projects is also a requirement. Don't expect ot give the child a verbal list of 'chores' (like clean and organize bedroom) once or twice and get frustrated a couple hours later when you discover your request has been ignored. Check on the child (they get distracted remember), see how she's doing and be ready to give suggestions and assistance. Even do it with her a few times so she knows exactly what is expected in the task and where and how things go. If her room is fill of more toys (due to endless gifts ect) than she needs plays with and/or has room for, downsize what is in the room. Give little played with items away, keep a specific area in room with a toy box or tub for her most enjoyed toys. Give her shelving to display 'treasures', a couple drawers to keep all the tiny things that all kids seem to 'collect' but have no space (and usually even a need for LOL)

And stay on top of it. Don't expect for child to clean room (and clean it to expectations) if the room has been let go for weeks. Mom needs to pop her head in the room and give reminders about 'lets get this picked up before you get anything else out'.

"I'll help you out by doing one of them. Which would you like me to do? Make your bed? Clear your desk? Straighten your shelf? Or put away the laundry?" (Now she's heard the tasks twice.)

"OK, you want me to make your bed? Great! I'm happy to do that. Now, which one of your jobs would you like to begin with? The desk, the shelf or the clothes?" (That's now three times that she's heard what to do, all in a pleasant manner, and one thing is already off HER list, so she already feels like this isn't so bad.)

"The shelf? Good choice! Let's see you get your books all neat and tidy in a row."
(Once she begins, you start pulling off the bedding. Look at the clock.)

"Wow! You're making great progress! You're practically done your shelf and it only took you two minutes... ... ... Holy moly, one job down, two to go and that only took you three minutes! Would you rather do your desk or the laundry now?"
(You see how there's continual feedback and encouragement? The ADD brain can't self-reward, so a child with ADD needs external support to produce the positive neural response that a typical brain produces on its own.)
(Once she starts doing the desk, you start getting the fresh sheets on the bed. Look at the clock.)

"Tell me about what you were colouring this morning?"... ... ... "Sounds cool! When we are done this tidying, I'd love to see it. Hey look! You're finished putting your colouring away and it took less than four minutes! I might just have to rename you Speedy Gonzalez! Just one job left, do you remember what it is?"
(When she begins putting the clothes away, you start putting her comforter back on the bed and fluffing pillows. Look at the clock.)

"That's quite a lot of clean laundry. I have an idea to make it go more easily. Would you like to hear it?"... .... "No? OK, that's fine. I bet your plan will work just fine." (If you offer a plan and she declines, let her do it her way. This isn't something where the method really matters.)

"There! I'm all done making your bed. Can I give you a hand with this last bit of laundry?"
(Follow the lead on how she was doing the task. If she was making a pile for closet and one for drawers, go with it. If she was going by colour, go with it. If she was going in order of pulling from the pile, go with it. Don't bowl over the sense of accomplishment she's getting from it by intimating that she's doing it wrong.)

"Whoa! Your room looks a kabillion times better and thdat only took us 11 minutes. I am so impressed at your hard work! Doesn't it feel good to have a clean bedroom? I can hardly wait until the next time I stroll down the hall and see this. In fact, I'm going to walk down the hall right now, just so I can look in your door at your nice room." (Make a big show of strolling down the hall to ooooh and aaaah when you look in her door.)

I know it sounds like a lot of work.
But you know what else is a lot of work? Getting pissed off because your kids are being dreadful, their rooms are messy, they're stalling on doing it because they don't know how and it sucks to go clean your room all by yourself. Frankly, I'd rather clean SS's room with him and put a lot of effort into encouragement and positivity than put at least that much effort into fighting and punishment.

Thanks for posting that.

One question though - I thought having a kid clean his room before something awesome like ice cream or games would be more of a incentive to get his room cleaned?

Also your food container idea sounds excellent, we buy a bunch of snacks for them for the entire month but their food habits pretty much suck, we make food easy for kids to eat but they prefer sneeking and grabbing cookies and other snacks that should be just a snack for their afternoon or after eating lunch, or you know, just to entertain their stomachs, not to eat the snacks the entire day.

Again, would trully appreciate any suggestions you have.

He too complained that my dd would get out of bed with excuses after putting her to bed. I had to remind him and prove to him (by asking his own mother) that ALL kids find reasons to get up from bed until they learn not to. Consistency is key. You have to put them to bed not send them to bed. I noticed that once we started doing a real bedtime routine my dd would stay in bed. Meaning we did the same thing every night and we both give hugs and kisses and tuck her in.

Everyone can't stand this child. No wonder she is so badly behaved. She probably can sense this and so being good will do her no good at this point. She gets more attention when she acts up than when she is good so acting up gives her what she needs.

Love Ceph's advice. Take it. Find a way to love this girl. Be the man in her life that she doesn't have biologically. She needs something and with research and understanding. You could be that for her. Sounds like you are on the right path by getting medical and psychological help. Keep it up and be the difference for this little girl. It can't be easy to be hated by everyone in your life.

- She's running at the pool. Instead of yelling "Stop running!" across the pool deck, yell "Walk!" and then say thank you when she does it.

- You don't want the TV on in the morning because you'd like to enjoy some quiet with your coffee and your email. She strolls out to the living room and you know she's headed for that remote. Say "Leave the TV off please. I'd like some quiet for about half an hour. Would you like me to tell you when you can turn it on?"... ... ... "OK. In the meantime, why don't you go get dressed and brush your teeth? Then you can play or read until I'm ready for the TV to go on." Now, follow through, when about thirty minutes have passed, go to her and say "Thanks for being patient and giving me some quiet to check my email and drink me coffee. I REALLY enjoyed it! Anytime you want to pick up your toys and come watch TV is fine."

- She's whining and you're finding it annoying. Instead of saying "Stop whining," calmly and quietly say "I know you're feeling tired/frustrated/lonely/hungry/bored/etc, but I'd like for you to speak in your usual voice to tell me what it is that you would like."
When she improves her tone a bit, say "Oh, that sounds so much better! Yes, we can have supper soon."

- She and her brother are horsing around and she gets too rough with him. Say "Be gentle please. Pulling on his arm like that could dislocate his shoulder," instead of "Don't be so rough."
And when you notice that they are horsing around appropriately, acknowledge it and say "I like seeing you two play well together."

Another is to drop the questions "What are you doing?" "What were you thinking?" and "Why?"
If she's doing something she shouldn't be, don't waste your breath saying "What are you doing?" you can obviously see that she is standing on the back of the couch rubbing her jam-covered hands on the wall (a real life example from when my SS was her age). Don't blow your top, just matter-of-fact-ly say "Get down from there please."
Now that she's down, suggest washing her hands and getting a cloth to come clean up the mess.
She probably wasn't thinking anything at all while she was doing it. She probably has no reason why. You'll just be mad at one another with the exchange of "What were you thinking?" "I don't know."