Either and vs. Either or

Solution 1:

Yes, you're right that the correlative conjunction either ... or ... is simply a summation of successive or's -- either ... or ... or ... or ..., with only the last or obligatory. Same thing without either, except that then it's not clear that this is disjunction with or, instead of conjunction with and (which is more common, and unmarked). But if you start the list with either you don't need to include and stress or all the time.

Either ... and ..., on the other hand, is simply wrong, and probably just a typo if written.

The answer to the second question is that

• any one of a, b, c, and d is mathspeak for any (or some) member of the set [a, b, c, d]

while

• any one of a, b, c, or d is not mathspeak, but simple enumeration, with "free-choice" any.

Solution 2:

Your understanding of "either a, b, c or d" is correct. But with either, we never use and. Hence "either a, b, c and d" is incorrect.

"any one of a, b, c or d" means one among a, b, c, and d.

"any one of a, b, c and d" seems vague.

Solution 3:

I'm a mathematician, and I'd just like to confirm that, although some of us have a reputation for mangling the English language, I've never encountered the "either ... and ..." mangling before. I'm inclined to assume it's just a typo.

Solution 4:

either a, b, c, and d

This means that possible combinations include ad, bd, and cd.

either a, b, c, or d
any one of a, b, c, or d

Both of these mean that the possibilities are limited to a, b, c, or d.