Neither/Nor vs. Either/Or

Neither/Nor

Follow "neither" with "nor." Usually, "nor" follows "neither" in the same sentence, as in, "neither A nor B." Together, this neither/nor structure forms a correlative pair. This means that the information one term introduces is connected or related to the information the other term introduces.
The two terms can be applied when discussing actions or they can be used when listing nouns.
Example: "He neither listens to music nor plays it."
Example: "She likes neither candy nor cake."
Note that “neither” can also start a sentence.
Example: “Neither Sarah nor Jim can make it to the party on Saturday.”

Use “nor” multiple times within a list. Typically, the neither/nor structure is only used when drawing a negative connection between two objects or actions. You can use "nor" when talking about more than two ideas, though, but you need to repeat the word "nor" after each item in your list.
Note that "neither" is only used once, no matter how many times you use "nor."
Do not merely separate the items in your list by commas.
Correct example: "The store had neither peanut butter nor jelly nor bread.
Incorrect example: "The store had neither peanut butter, jelly, nor bread."

Either/or 
Either / or - used in a sentence in the affirmative sense when referring to a choice between two possibilities

Example: We can either eat now or after the show - it's up to you.

When using either/or note the following rules:
1. If both elements are singular, then the verb is singular too.
Either the father or the mother has to attend the meeting. (father and mother are singular; so the verb has is singular too)

2. However, if one of the elements is plural, then use a plural verb.
Either Sue or the girls are going to prepare dinner tonight. (the girls is plural; so the verb are is plural too)