OP here, gosh 5 pages of replies already. I do appreciate everyone's opinion and glad to know many don't think I'm a prude.

Or even if I am, "our house, our rules." But those of you who disagree with me, that's fine too, I appreciate everyone's opinion.
I think what bothered me MOST is that we had never even met this girl. I don't think he's been seeing her long at all, in fact it's only been in the past couple of weeks that he has even mentioned her. And he waits until we are GONE before he brings her over and then has her spend the night. She was still here when we got home from our weekend up north, so he did introduce me to her then, but still.... I just feel it would have been nice to get to know her a little, have him bring her around a few times, etc. BEFORE having her spend the night. I MAY have felt a little differently about the situation if that would have happened, I don't know.
I do respect the fact that he didn't have her stay over when his kids were here Friday and Saturday nights. To my way of thinking that was more respectful to his kids at least. They don't need to be subjected to that.
And to those who think our relationship is "odd", I would love to hear why you feel that way. Our son has been on his own since he was 18, it was only since last September that he let his house go (so he didn't have to pay rent) and started staying here with us once a month when he was home from his trucking job. We agreed to let him stay here, it was all worked out before he even took the job. We agreed it didn't make sense for him to pay rent and utilities when he wasn't there.
Then when the trucking job didn't work out (no money in it) we talked BEFORE he quit, and agreed to let him live here until he could get his own car again and another job. We just didn't know it would take so long and there have been some strained moments, but I think that would happen with ANY family who had an adult child move back in with them.
I guess I just don't see what is so "odd" about trying to help him get back on his feet.

He doesn't pay any rent, utilities, or pay for groceries. He is living here completely free. Now if he WERE paying rent, etc. then having the girlfriend over probably would not have been an issue. But anyway, hopefully this new job will work out and he will be able to get his own place again soon.