It is me (or it's me) is considered an informal style. Today, most native English speakers use It is me instead of It is I. Me is usually an object pronoun. In most cases this means it's on the receiving end of the action in a sentence.
'It is he' sounds very formal. 'It is him' is grammatically correct and is in common usage. HE is used for subjects and predicate nominatives. HIM is used for objects of preposition, direct objects and indirect objects.