Here's what i gathered, but i use time cheats a lot, so randomness and broken things abound.
You get invited to the party if you have a good relationship with Anya, regardless of whether you completed the Roma chain or not. The trigger might be meeting Roma specifically, but i'm not sure.
Other than the first time, every party is once every other week, regardless of Anya inviting you every week. So if you get invited the week after the first party and the invitation doesn't happen when it should, check again next week same time, even if she says "missed you at the party" in the meantime. Don't try to get yourself invited again.
Due to initial coding, there may be issues with the party trigger if you get invited on tuesdays of thursdays so avoid interacting with Anya on those days until someone who knows better says otherwise.
Save scum doesn't help. You either get invited or you don't.
And as a side point, don't be slutty if you wanna start the Rex chain. Not sure about lesbian orgies, but the other guys at the party are a no go until you finish the thing.