'Either … or' is used in sentences in a positive sense meaning "one or the other, this or that, he or she, etc." in other words it is used to offer a choice between two possibilities
Examples:
I’m not sure where Laura is from. She’s either German or Italian.
Would you like tea or coffee? - Either. I don’t mind.
There are two ways from here to the airport. You can go either way.
'Neither … nor' is used in sentences in a negative sense meaning "not this one nor the other, not this nor that, not he nor she, none of them etc." - in other words it is used to deny both possibilities
Examples:
Is your friend British or American? - Neither. She’s Australian.
Neither of the restaurants I went to was (or were) expensive.
Neither Mike nor my other friends care about their future.