Is "each and every one of you" singular or plural?

It's singular. It's exactly the same as "each one of you."

One is singular, so one of you is singular, so each and every one of you is singular.

It's singular, but it does not refer to one person from the group -- it refers to all the people from the group, individually.

Possible alternative answer:

If it were “each one” or “every one”, then the verb would be conjugated according to one, which is singular. In either of these scenarios, it would be “each one is” or “every one is”, others have said.

One could also interpret “each and every one” as being plural, with two subjects: “each [one]” (one is implicit) and “every one”. Just as “Billy and Susie are”, “each [one] and every one are.”

This latter interpretation, while grammatically self-consistent, is likely incorrect (and ambiguous!) in most situations, because “each and every” is a compound determiner or pronoun. In this case, as others have said, the subject (“one”) is singular, and the verb should be conjugated accordingly: “each and every one is”.

It is more common in modern English to hear “each one” or “every one” than “each and every one” because choosing one or the other and removing the “and” avoids the grammatical ambiguity described above.