How can Angel enter Russel's house? He wasn't invited in. Are the homes of vampires not covered under the "invitation only" rule?
All of that's true, but there's one more very important thing to consider. At that point in the show, Joss and his writers hadn't decided that Angel was going to be a vampire. Therefore the invitation rule for vampires wasn't an issue, and they either forgot once that decision was made or thought that the fans would,