With the caveat that I'm not a metal professional, I'd use some WD-40 on it. Is the entire thing metal, or does it have a handle made of wood or some other material?

There are lots of metal cleaners out there.

It's got some kind of a handle that is something brown with texture. I would like to take it a professional rather then do it myself. I don't think I can clean out the inside. I would need like a sonic wave cleaner. Do anyone do this type of cleaning?

Reading the OP I wondered if the jeweler might do it. I seem to recall that jewelers and opticians once had ultrasound cleaning appliances back some few decades ago.

Inside the chamber where the blades fold in, it's like a pocket knife, but it so very small. I can't get in there to clean.

Bring it to a reputable jewelry store with bench jewelers onsite. They have the knowledge and professional equipments, such as bench equipments, jeweler's hand tools, ultrasound cleaner and steamer...etc, to do the job. They also have liability insurance.

You may want to talk to a few jewelers and their customers to find a good one. In an average income neighborhood, I found a great jeweler who does fabulous job with incredible reasonable price.

There are a lot of jewerly stores in the malls around here that clean rings and such, so could try one of those today.
I live in san francisco, so I can't drive to London at all.