So I was sent by the NCR to go kill or convert the Great Khans, so I went into the longhouse, killed Papa Khan, and everyone went hostile so I just killed them all. Then I killed all the grunts in the immediate area, but my quest section still says I need to convert or kill the Khans. What should I do? Has anyone else encountered this?

Have you tired simply returning to Col Moore? Where is your active quest arrow pointing you?

Yeah, I greased the punks myself. For some reason we're supposed to feel sorry for them, but they're just a bunch of scum raiders who keep pissing off the NCR and keep getting wacked. Wasteland's better off without them.

That's the weird thing. The quest arrow points me to the door in/out of the longhouse. So if i'm outside, it says to go inside, and if im inside, it says to go outside. Tried talking to Colonel Whatsherface and the quest was still in progress. I'm kinda stumped...

I believe that the Oh My Papa part of that questline begins after you run through the dialogue with Papa and then speak with Regis and run through that dialogue. You exit the Longhouse and Regis comes out to speak with you. If you've killed everyone, it might be over for you. It's a very convoluted path to get through that quest, one of the buggiest in the game, unfortunately. It ended my first game before the patch and the patch didn't help it. I think you'll need to load an earlier save. See the wiki for details. http://fallout.wikia.com/wiki/Oh_My_Papa

See, that's completely messed up! It says to kill them if they don't cooperate. They didn't cooperate, so what's the logical conclusion there...?

You have to walk all the way to the end of Red Rock Canyon where there's the training grounds and wipe out the rest of the Khans down there, then the quest will update once you've "destroyed" the Khans.

Same thing happened to me last night.. except as soon as I stepped in the Longhouse everyone (except Karl for some reason) was immediately hostile towards me.