"Neither them nor us" vs "Neither they nor we"

Solution 1:

The correct answer is

"Neither they nor we went to the show." (Neither modifies the subjects; if the subjects were not named, it would stand in for the subjects, but in your case, the subjects are named, and neither/nor both require subjects, therefore cannot be the subjects of the verb went.)

They and we are compound subjects of the sentence, therefore are in the nominative case; they and we are doing the action of the verb.

Them and us are in the accusative case - recipients of the action of the verb, or objects of a preposition:

We hit them. (direct object of the verb) The agreement was between them and us. (objects of the preposition 'between')

The Nominative (or subjective) is the form nouns take in the dictionary. I (accusative: me), we (accusative: us), he (accusative: him), she (accusative: her), they (accusative: them) and who (accusative: whom).