the correct form of your sentence is:
there weren't any hairdryers, shower gels and shampoos in the room.
none of your sentences is correct and here's why:
whenever any is accompanied by conjunctions the verb is plural. both shower gel and shampoo have countable and non-countable forms, but in this context, countable forms make more sense because you're probably mentioning shampoo bottles and shower gel products
your sentence is about three items, shower gel, hairdryer, and shampoo. you can not use "neither" for more than two items. so the correct form of usage of "neither" in this case is:
there was neither hairdryer nor shower gel in the room (you have to get rid of one item).
also "neither" is singular and should be accompanied by a singular verb, so "was" should be used in this case.
