We use the "if (past tense)..." form to indicate a possibility which is unlikely or unsure. It's an imagined situation. He's using this form to avoid putting a direct demand towards the listener, so the general effect is that is sounds polite. The full line "...if you wanted to come hang out with us, you could" fits the regular second conditional pattern. "If you want..." indicates a strong possibility (or desire) for it to happen. In a request or invitation, this would put pressure on the listener to agree.

Hmm, it's a little bit difficult to explain of course but, I'll try my best. In my opinion, "If you wanted to hang out after school or something..." sounds more polite than "If you want to hang out after school or something...". Or looked at a different way: "If you want to...." sounds a little bit like you're assuming they want to. Where as, "If you wanted to...." sounds more like you are only making a recommendation, but you are not assuming that they want to. In Spanish this is done with the "subjunctive" tense which basically means that you are trying to indicate that there is some small amount of doubt or uncertainty. I hope it helps.

The sentence is wrong! She says: Do you want TO.... not "wanted" And of course the lousy typing style. They only compound the errors further.