In general, use 'into' when movement, action or a transformation of state occur. 'In' indicates location or state that is generally more static and not transitional. For example, She liked sitting in her grandfather's chair is correct. She liked sitting into her grandfather's chair is incorrect.

In casual English conversation, into and in are often (but not always) used interchangeably. Native speakers often don't worry about the small distinctions in grammar points like this. You will be understood even if you make a mistake, so do not stress yourself over this point unless you are preparing for a test. The distinctions in meaning in your first two examples are very small. "It's funny trying to translate that into any language" means it is funny to take the phrase from the original language and translate it to another language. "It's funny trying to translate that in any language." Is saying that the particular phrase is funny to translate, no matter what language you encounter it in. Regarding the third example, it is very common to hear people use both in and into in such a case. I cannot explain any distinction, if it exists at all. However the final example you give, "She is not into dancing." is a different case. You CAN say "She doesn't like dancing" and it has the same meaning. To be "into something" is a slang phrase that means you have interest. To be "not into something" means you have no interest. I hope that's helpful!

I think that you want to say that it is "FUN" to translate something into another language. That is, "fun" means "enjoyable." "Funny" means that you are laughing. In my opinion, translation is a lot of fun, but usually it is not funny. It is hard work.