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 for several hundred years.
rigid enforcement of antique decorum will help neither language, literature, nor literati
Origin and Etymology of nor
Middle English, contraction of nother neither, nor, from nother, pronoun & adjective, neither — more at neither