Q:

he is he or him- they are they or them?

They are they/them
He is he/him

Which ones are correct?
Is there some sort of agreement rule because for ex- we say it is he, so would we also say "they are they" or "he is he"?

A:

"They are they" and "he is he" are the correct forms because the verb "is" is a linking verb.
As a linking verb, the verb "is" doesn't take an object, which would require the objective case pronoun for your predicate, i.e. "They are them" and "He is him." Rather, it takes a subject complement, such that you end up having to actually use the subjective case pronouns "they" and "he" (again, in the case of your less commonly used sentences).
More commonly, however, if you pick up the phone and someone asks if you are Sol, you'd say, "yes, this is he," for the above reasons. Also, if you were to enter a room swinging a big something and wanting to identify yourself for whatever reason, you'd announce, "Everybody, it is I, Sol."

