Hello, hope! Jumping in on this particular bit. Just wanted to point out that those two phrases you've used here, they are not slang. They are idioms. Since I'm not a language teacher my attempt to explain idioms will no doubt be clunky (now that qualifies as slang, lol). An idiom means something different to the meaning of the individual words in the phrase. So, as you now know, the phrase 'not my cup of tea' usually has nothing to do with tea or hot beverages but refers to our preferences, likes, dislikes etc. An idiom has to be learnt as an entire phrase, you can't break it down to the individual words. It just won't work.
Slang doesn't have to be offensive but it is always informal and it's more likely to be used verbally. Not often used in writing unless you're communicating with a friend (or maybe, these days, online).