doggone
1851, Amer.Eng., a "fantastic perversion of god-damned" [Weekley]. But Mencken favors the theory that it is "a blend form of dog on it; in fact it is still often used with it following. It is thus a brother to the old English phrase, 'a pox upon it,' but is considerably more decorous."
Others have it derived from the Scottish dagone, or "gone to the dogs," but there's a bit of debate about that.
From my own search, I found several pre-1851 uses. It looks like it may have first appeared in print in a British publication, albeit of an American vernacular dialog, in Adventures in Mexico and the Rocky Mountains by British explorer George Ruxton, 1847 (date check):
It subsequently appeard three times in 1848 in Blackwood's Edinburgh Magazine, in articles written by Ruxton while living in America.
As Robusto comments, it's probably just an obvious turn of phrase that could easily have been "re-coined" repeatedly.
As Google NGrams shows, the term had no real currency until the 1980's, but that certainly doesn't mean such bands didn't exist (see this site).
Personally I think that it's quite possible many parents of wannabe rockers (esp. perhaps West Coast Americans) may have used it to describe what their kids get up to on the weekend, even back in the 50's. But it didn't really gain traction until the post-punk era, when the type of music associated with it started to become commercially significant.
Umpteenth comes from umpty, meaning an indefinite number. Etymology Online says "umpty" is derived from "Morse code slang for "dash," influenced by association with numerals such as twenty, thirty, etc."
And I think the "teenth" insert is to make the "th" easier to pronounce for the ordinal formation, but it might be also to add emphasis by way of lengthening the word. Also, it might be because of the teen/ten connection I mentioned in my comment above: an indefinite number of tens.
And this source suggests that Morse code slang word "ump" is imitative in origin, so I gather that means that that's what a dash sounds like in Morse code.
It occurred to me that this means something like _th times, then, or the equivalent of nth times (to the nth degree?)—although a single dash is Morse code for T.
Best Answer
From Etymonline:
Others have it derived from the Scottish dagone, or "gone to the dogs," but there's a bit of debate about that.
From my own search, I found several pre-1851 uses. It looks like it may have first appeared in print in a British publication, albeit of an American vernacular dialog, in Adventures in Mexico and the Rocky Mountains by British explorer George Ruxton, 1847 (date check):
It subsequently appeard three times in 1848 in Blackwood's Edinburgh Magazine, in articles written by Ruxton while living in America.