No idea how or why this is happened, but it was kinda neat. I was in junktown and I agree to take out the skulz gang or whatever they're called. I arranged to take them out with the head junktown guard guy. After agreeing to do this the game takes me straight to the skum pit bar. Vinnie is there and is killed very quickly. I take his pistol, knife, and leather jacket.

Nothing happens. No EXP for defeating the gang or doing the quest, nothing. I go back to the inn, Vinnie is there in his usual spot. I go back to the head guard and I am able to start this whole thing all over. I killed Vinnie like 4 times, each time with the same results. Kinda lame I guess that it won't let me complete the quest, but also quite nice to essentially have an endless supply of goods. I essentially can gather an infinite amount of wealth solely from this, which is cool this early in the game.

On the negative side, my fallout game keeps crashing, not to the point of it being unplayable but still pretty annoying if I haven't saved in a while. Wasted quite a lot of time killing Vinnie repeatedly.

Yeah, that head guard seems to self-replicate even in a proper playthrough. He'd kinda bugged, ain't he!
Next time, I recommend finding a different way to get rid of the Skulz. Or you can try this again; I've just never done it this way, so I don't know for sure if this is a common bug.