I'll try and make this short. A girl will be with her girl friends and a some guys at a table, I'll be walking past them, and I can see the girl waving me to come over. To me this seems odd. Why would she want me to come over? Also, with her hanging out with a bunch of dudes, I can totally see one of 'em saying "Get lost!". This has happened to me before. So I just walk by, and ignore them. I'm trying to understand why would they wave some stranger to come over?

She's into you. If you don't feel like sitting down with the group, motion to the girl to "come here". If she doesn't come, so what. Nothing to lose.

Another way to do this without engaging the group is you can go up when she calls you over and completely ignore the table and talk to the girl only. The others mean nothing to you - you're interested in the girl.

Another way to go about it is to go up to her and slightly engage the group but be focused 85% on her.

Yet another way is to go up and be bros with the guys and treat the girl like a bratty little sister.

And there are undoubtedly many other ways.

I've been in the same situation and learned from the mistakes:

A cute girl asked me for a ride, that was her opener "can i get a ride?" but she was with 2 friends, a male & female. I pretty much ignored her. She didn't give in: "Are you going to X (suburb)?" I basically ignored again. Bad move. A better move would have been to engage her a bit and feel out the situation.

In another instance I was walking by a minivan; a girl was in the driver's seat; some dudes in the backseats. She motioned me over and waved at me. I ignored (because of the dudes). Again, I've learned from this - go up and get a sense for the situation and who knows what may come of it.