I think tweak and yank are somewhat like slang, so I would use caution and not use them in an essay, but in common speech they are fine. Yank is like pull, but pull can be a gradual motion, yank is usually abrupt. Twist implies a turning of one part the object while the rest stays in place, so it gets usually deformed. It can be done while you pull it, or you can also not pull it, just twist it where it is. You are usually deforming it by turning. So we say "twist words", that is to say, change their meaning, like when you partially misquote someone and make it look like they are saying something else.

Tweak is used in a lot if various ways. For example " I am going to tweak this recipe by adding in more sugar". " I tweaked(could also use twisted or pulled) my back doing yard work". "I can't open the door because it is tweaked in the doorframe. I tried pulling it, I am going to have to yank it really hard"