Although use with or is neither archaic nor wrong, neither is usually followed by nor. A few commentators think that neither must be limited in reference to two, but reference to more than two has been quite common since the 17th century <rigid enforcement of antique decorum will help neither language, literature, nor literati — James Sledd>.
Origin of NEITHER
Middle English, alteration (influenced by either) of nauther, nother, from Old English nāhwæther, nōther, from nā, nō not + hwæther which of two, whether
First Known Use: 12th century
: not the one and not the other of two people or things
Some commentators insist that neither must be used with a singular verb. It generally is, but especially when a prepositional phrase intervenes between it and the verb, a plural verb is quite common <neither of those ideal solutions are in sight — C. P. Snow>.
Examples of NEITHER
“Which one do you want?”“Neither, thanks.”
Neither of them dances well.
There are two flashlights, neither of which works.