Because we were newbies and ignorant, we ended up painting our kitchen with some cheap $5 reject paint from Sherwin Williams. Well, five years and two kids later, the walls are a disaster. I bought a nearly identical colored (but semi-gloss) paint that we have gradually been painting the walls with. It looks much better, but we've held off on the two walls that have terrible stains on them.

Another dumb mistake was that I had a shelf with my olive oil on it. Well, some of the oil got on the wall. I tried to clean it, then primed and re-painted the spot. Of course the stain came back through again. Since then I have cleaned with TSP and sanded. Now I can't even tell if the stain is still there, but I'm worried about repainting the wall, for fear it will still be there. I have an oil based stain primer that I can use, but I guess my question is - do I have to prime the whole wall with it, or can I just prime the stain? There are other stains on the wall, and I can't tell if they are water or oil stains. TSP didn't take those out either. They don't seem as bad as the olive oil stain. Can I be semi confident after sanding and cleaning that when I use a semi-gloss it will look okay?

Oh, and my oil-based primer says not to use TSP. Why? Overall I was unimpressed with the TSP and am not sure why I even bought it.

Thanks in advance for any guidance you have for me moving forward.