They're actually not completely illegal. You need an NFA stamp for things like full automatic rifles, machine guns, most silencers, short barreled guns, and the stamps are often very expensive. Which is why you probably don't see many full automatic AKs being used in crime.

They are not in most US states. Not federally as long as they were manufactured prior to 1987. That's what makes them expensive; limited supply.

Here is a class I took on the MP5:

https://youtu.be/Vr8G0uXf19A