The U.S, America, or the States?

Whenever people ask me here where I'm from, I stutter.

"the U.S." I say. "USA. America." I continue, "the states."

I have a problem saying the U.S. because I think it sounds weird. So does USA. And saying America sounds equally strange. But 'the states' doesn't cut it either--only when I've said the other two does it sound right.

I just can't figure out which one to pick. Am I extremely alone on this one?

p.s. Stay tuned for a post on how to cross the street in Denmark..