As an asian, I'm confused!

Referring to your title, "I didn't do nothing" implies that she did not do nothing. Which means she did something. Not and nothing are both negatives and they cancel each other out, making it positive. Sorry if this is confusing.

Though it can be used to express the impossibility of something such as "How can you not not like beansprouts?"

It's like in maths when you have two negatives like 21 minus negative 5 it becomes 21 PLUS 5 because two negatives cancel each other out. Like that, I didn't do nothing implies that she actually did do something

Movie?

Yeah right