Response: "I'm doing really great! How are you?"
If the person is doing well, then that is great, but I haven't been "great" in 8 years, so this response actually means,
"I feel pretty bad, but I don't want you to know, so I am going to give you a noncommittal super overly excited answer and then deflect back to you" They will probably smile at you and be really convincing that nothing is wrong, but when it comes down to it, they just aren't comfortable sharing with you at the moment.
Response: "I'm okay..."
This means, "I feel bad, but don't know how much you actually want to know, so I am going let you ask a follow up question if you are really interested...." If they don't ask a followup question, then no harm done, but if they do, it means they are interested in what you have to say and willing to pursue answers.
Response: "I'm hanging in there."
This one is my personal favorite and it means, "Well I'm still alive, but I don't really feel like sharing all the gory details with you because I am tired and all the detailed would make you tired, so I am just going to smile and say "I'm hanging in there." This one lets you know that I really am not doing well, but doesn't really invite more questions and instead adds a bit of humor to an otherwise humorless situation.
Response: "I feel like crap"
This one is just the plain and simple truth. I feel like crap and I don't care who knows it!
So there you have it, four common answers decoded in all their guts and glory! See how are really is a complicated question both for the sender and the receiver so hopefully this helps next time you ask someone "how are you."