They all pretty much mean the same thing, with differing levels of sexual overtones. From the least crass/sexual to the most crass, it is: (1) to hit on someone, (2) to pick up someone, and (3) to hook up with someone. (1) and (2) can be rather benign compared to (3), which has the definite meaning that you want to have sex sooner than later. I would *NOT* use "are you hitting on me?" except in very limited circumstances. For example, if a guy comes over and says "Hi, my name is John. It is a nice evening, isn't it?" This is obviously an attempt to get to know you, but if you say "are you hitting on me" right away, you *are* being rude. Usually you try to show you're not interested in a less obvious way when someone is at least nice in the way they try to hit on you. The world is what it is because men and women meet and fall in love and build a family together. However, if a guy comes up to you and is rude himself from the get go, like, "hey baby, where have you been all my life? Come up to my hotel room," then you don't even have to dignify that with a response. Just walk away. So personally, I'd say there are only very limited circumstances where you'd use "are you hitting on me" without being (1) rude or (2) full of yourself (as in, "I'm so beautiful that of course you must be hitting on me."

To "hit on someone" typically means that you are flirting with someone with the intent to enter into a romantic relationship with them. This can be applied to both short and long term relationships. To "pick up somebody" means to try and find someone to have a one-night stand with. To "hook up with somebody" means to have a one-night stand with.