I think that people develop a natural feel for sarcasm. When somebody doesn't want to say something negative, they say something positive instead. For example, if someone has a really cruel dog that's always going around terrorizing the neighbors after work, and that same someone says, "I love my dog. She's such a sweetheart!" A sarcastic remark would be, "Right, she's a real angel!" If they don't use the tone, then you could consider it 'dry' humor.
Sometimes people also like something a lot and say that they don't. For example, sometimes women start hitting their boyfriends after they propose and say, "I hate you," even when they are obviously happy and excited.
Humor seems to be in timing. So, it's probably the set-up more than the response that makes sarcastic humor so great. Some people seem to live on sarcasm. Everything they say is inverted. I find this terribly annoying. Like any kind of joke, it's funny for a while and then gets old. One-word replies, like "Hilarious," don't have to be sarcastic. Neither do 'way-to' sentences. They're probably common because there are really good set-ups. It's even idiomized in the phrase "famous last words".
A side note..., this question might wind up being very chatty. I still think it's cool, though, because it seems like it's coming from an AI scenario writer or something.