If there are two singular nouns, it's all right to say:
Neither my sister nor my brother likes / like pizza. Neither Susan nor Mark likes / like pizza.
(plural form of verb is informal)
Even if the nouns are in two different forms, it's also all right to say:
Neither my friends nor my sister likes / like going to parties.
However, try to put a plural noun after nor and use a plural verb form:
Neither my sister nor my friends like going to parties.
If there are only plural nouns, use a plural form of the verb only:
Neither my siblings nor my friends drink lemonade.
And what if there are only pronouns used?
Here's the answer:
Neither she nor he was keen on judo. Neither she nor you know me. Neither you nor I am responsible for the failure.
The rule says - the pronoun that is closest to the verb determines the use of the form of the verb; and try to put I as the second element of the construction - it makes the sentence more readable and more polite.