"Geek" and "Nerd" are both okay, but "geek" is a little better here. "Nerd" subtly implies that someone's passion is something educational. A person who studies invertebrate biology, or latin, or calculus, for fun is a nerd. "Nerd" can also be used to describe excellent students. A person who can name every single character from their favorite show or collects anime figurines is a geek. Again, though, the difference is subtle, and you can use them interchangeably. No one will question it or think less of your english. I've never heard the term "anorak" before. I looked it up; it's apparently British? If you use it in a conversation with an American, they're unlikely to understand you. It's worth noting that the word "otaku" has been adopted by some hardcore english-speaking anime fans. Your average english speaker wouldn't recognize it, but college age/high school age geeks might.

I'm not sure I've ever heard 'anorak' used in that way. Nerd and geek mean essentially the same - I would say that 'nerd' is a bit more "serious" than geek is. I can't speak for Japanese culture, but I know that it's currently quite popular to have nerdy/geeky traits in the West. It's common for "normal" people to self-describe as a geek/nerd, rather than either word having their old meaning. We don't really have a dedicated word to describe someone who truly spends too much time on a hobby any more, although we do have insuts for specific hobbies.