huh...to me is the same as what?? (neutral)
hunh is more "Well what the heck are you talking about now?" with a trace of exasperation or disgust behind it...
Me too, but I'd come to think of "huh" as being less polite than "what" or "excuse me?" and tried to avoid it. But the hell with politeness!

We're reclaiming the word.
When I use it, it's in either "what?" or "what the heck are you talking about?" senses that you mention, Jess. Those are the ways it sounds most natural coming out of my mouth. But when Ennis says "hunh" it usually means, "don't you agree?" He tacks it on the end of a declarative sentence, the way Canadians say "eh?" As in, "That snow barely stuck an hour, hunh?"
Or sometimes (referring to SpookyRabbit's EDM Catalogue -- thanks, Spooky! And thanks, Meryl, for linking it!) he says it to drive home a question, as in "What if Aguirre finds out, hunh?"