。
She called to invite me to her house.
Literal
She [topic-は] me [to-に] house [to-に] invitation's phone-call [object-を] did-[toward me-てきた].
Two に particles in a row, doing different jobs: 私に (dative recipient — 'to me') and 家に (locative target — 'to (her) house'). 招待の電話 is 'an invitation phone call' — a phone call (電話) whose nature is invitation (招待). The auxiliary ~てくる on 電話する marks the call as directed toward the speaker — she called me, with the action moving inward.