invite someone into some place
and invite someone into bid or request someone to enter a place. Don't leave Dan out there in the rain. Invite him into the house! Oh, do invite in the children!
invite someone out
to ask someone out on a date. I would love to invite you out sometime. If I did, would you go? Has he ever invited out a girl on a date?
invite someone over (for something)
to bid or request someone to come to one's house for something, such as a meal, party, chat, cards, etc. Let's invite Tony and Nick over for dinner. Let's invite over some new people.
invite someone to something
to bid or request someone to come to an event. Shall we invite Sally to the party? I didn't invite her. She invited herself to this affair.