Having grown up in Illinois, I have to throw my own befuddlement behind "quarter of". I've lived in upstate New York for twelve years now, and I still get confused when someone says "I'll be over at a quarter of three".
I've never actually heard anyone say might could, or any other double modal, but it makes perfect sense to me, and I hope it spreads northwards. :-)
(Oh, and see this map for American usage of double modals.)
Sorry I didn't check back after my post for 6 days.
I don't think it sounds grammatically atrocious if your native dialect permits double modals. Something I hear in the Northeast U.S. that I am pretty sure is ungrammatical in every other English dialect is "a quarter of." The first time I ever heard the phrase was on an episode of "The Jeffersons" and I assumed it meant 15 minutes after the previous hour--which is what it seems to mean, logically. When I moved to New York I found out that it means 15 minutes before the hour, which is what in most dialects is referred to as "a quarter to" or "a quarter 'til." To anybody not from the Northeast U.S., "a quarter of" might sound grammatically atrocious, or at least bewildering.
I don't completely agree with U's assertion that "might could" substitutes for either word. It's really more like saying "I might be able to" as opposed to saying "I might if I feel like it." Like this:
Ned: "Lonnie got his tractor stuck in the gully. Could you pull it out?"
Lester: "I might could if he's not stuck too deep."
That's very different than saying:
Ned: "Lonnie got his tractor mired in the gully. Could you pull it out?"
Lester: "I might. What's in it for me?."
It's definitely a Southern regionalism which doesn't sound strange to my ears.
Most every time I hear the phrase, it's used in one of two ways: it's either substituting for might, or it's substituting for could. In those situations, I get the impression the speaker doesn't know which one is correct, so he goes with both just to cover all the bases. That's BAD.
But to be fair, there are other times it's used as an abbreviated form of "might be able to" and that's a little more acceptable. Grammatically atrocious, of course, but shorthand is reasonable in response to a mouthful of a phrase.
It's not redundant or repetitive. "I might could" means "maybe I could" or "possibly I could" or "I don't know whether I could or not" or "perhaps I could" or "maybe I would be able to" or "given the right circumstances I could." It may sound odd if you're not from the South or from Scotland, but it's a useful construction and it might even spread to other parts of the English-speaking world in much the same way that the way the use of "already" after the imperative has spread from certain ethnic dialects of New York City.