Should we have a house warming/party at all?

Once you are moved into the house and your parents have moved out, go ahead and have the party. Just call it a party, not a house warming. You could have a cook out or something and let everyone know that you just want an oppurtunity to host and event for the people you care about now that you have the means to do so, since you now have a new home. I think everyone will be happy to come to your party and see your new home.