either of them went to the party.
either of us went to the party.
They don't make sense, and capital letters are missing. Both of them went to the party. Both of us went to the party.
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They don't make sense, and capital letters are missing.
Both of them went to the party.
Both of us went to the party.
Neither of them/us went to the party.
You could use your original words as part of a longer sentence:
Godfrey wants to know if either of them/us went to the party.