Using neither in negative sentences?

Dear Mr. Toersten,

I thought that we can use ‘‘either and neither’’ only in negative sentence. But I saw in the movie that the dialogue use ‘‘either/neither’’ in positive sentence. When do we use either/neither instead of too/also in positive sentence?

Either he or Mike will go to the party. (One of both will go.)
Neither he nor Mike will go the party. (None of both will go.)[YSaerTTEW443543]

TOEIC short conversations: Asking whether a signed contract has been received[YSaerTTEW443543]