Are "betwixt", "trebble", etc., acceptable in American English?

"Betwixt" is archaic and highly marked for American English, but not technically wrong.

"Learnt" is non-standard, but intelligible and probably not a problem.

I've never heard or seen the word "trebble", and would mark it as an error in any piece of formal writing.

"Treble" (in British English at least) can mean the same as "triple", as well as high in (musical) pitch, as in the opposite of "bass" (see also the Wiktionary entry).

"Learnt" (again, British English) is an alternative past form of "learned" (Wiktionary again).

"Betwixt" is a great word, but is somewhat archaic (Wiktionary, one more time). Despite that, either "twixt" or "betwixt" was used in the film Serenity.

My $.02 USD:

Betwixt: not commonly used nationwide; I've heard it (and used it) in New England.

Trebble: We don't double up the b. It's spelled 'treble' and it is still in use.

In American English, we don't substitute the -ed ending on verbs with a t.

Learnt = learned Spelt = spelled

and so on.

Without wanting to speak ill of Texas... it's Texas. They have their own dialect of English down there.

As a bit of anecdotal evidence, my nickname is "Lin" (short for Linda). My Texas friends manage to take the letters Lin and somehow stretch two syllables out of them. "Le-in" it becomes. Why? I have NO idea.

I've never heard an American use betwixt, trebble (or aught, naught, or nought), or learnt, although:

"betwixt and between" as a figure of speech would be "acceptable".

"larnt" is an Appalachian dialect word that would cost you points in a school paper.