"Neither you and your girlfriend came, nor my dad, nor my mom."
In the sentence above, is it correct to use two nouns after the "neither". Or should it be: "Neither you came, nor my dad, nor mom, nor your girlfriend."?
The items following "neither" are supposed to be separated by "nor", so if you separate them by "and", then according to the "official" meaning of "neither", that changes the meaning: since different items are supposed to be separated by "nor", separating them by "and" suggests that they are one item: "Neither (you and your girlfriend came), (nor my dad), (nor my mom)." For a "neither" statement to be true, all of the items must be false: it must be false that your mom came, and it must be false that your dad came. If "you and your girlfriend came" is one item, then that must be false as a whole, rather than "you came" and "your girlfriend came" needing to be false separately. That is, if you came, but your girlfriend didn't, then literally speaking, "Neither you and your girlfriend came, nor my dad, nor my mom" is true. If you want to make it clear that no one came, you should use "nor" for all of them. If you actually did want to allow the possibility that one of "you" and "your girlfriend" came, then the wording presenting would be a bad idea, since although literally that's what it means, a reader could easily be unsure as to whether that's really what you meant, or you misspoke. Other wordings would be clearer, such as, "Neither my dad nor my mom came, nor is it the case that both you and your girlfriend came."
I would be happy with plural items after 'neither', and indeed after 'nor'.
Neither mother and father nor all the gods can be as gracious as the true Guru.
a considerable quantity of finance, which neither mother and father nor part-time jobs can present
Neither the King and Queen nor the Norwegian authorities were aware that such measures had been taken.
Neither husband and wife, nor brother and sister live in a community of labour
Neither husband and wife nor the Institute shall have any rights or obligations
Generally speaking, "neither" is meant to be used with two objects, and your examples are no exception. Neither of these two examples are "proper," but if you were to select one, the first would make more sense. Essentially, saying
"Neither you nor your girlfriend came"
Would be a less redundant way of saying
"You did not come, and neither did your girlfriend"
The second example you provided is rather nonsensical, considering the fact that there aren't two objects clearly being referenced. Who are the two which "neither" refers to? If it is still the girlfriend, how is a reader/listener supposed to infer that?
Altogether, I'd say get rid of neither entirely. It may sound better to simply say:
"You didn't come, nor did your girlfriend, mother, or father."
Though if you're attached to one of those two examples, I'd say the first is better.