I need some help getting rid of a body

Solution 1:

Grabbing and dragging them works, but as you've noticed, it's kind of slow. I find generally pulling works a bit better than pushing, so you might try grabbing and slowly dragging so as not to lose your grip.

It sounds like you've got a lot of cleanup on the horizon, though, so perhaps more drastic measures are in order.

You could Reanimate, but the easiest method of doing that is probably the Staff of Worms which is going to be hard for a level 1 Thief to get. If you had it, you could just cast it and have the not-quite-dead NPCs follow you somewhere else before the expire yet again.

You could also try some sort of magic, perhaps a fire-type spell that has a nice explosion effect. You can't really "aim" it as well, but hey, it's faster corpse movement, so there's that.

Alternatively, you could try traveling somewhere else, preferably a distant indoors environment, and waiting for a few consecutive days before returning. The location will tend to reset, giving you that "new home" feel and purging the corpse stink almost like magic. For best results, wait at least 3 days before returning.

Solution 2:

If you're playing on PC and don't mind using console commands, this should be relatively easy. Open the console (`, § or ~ key depending on your keyboard - the one below Esc), click on the body, type in "disable" and hit enter. Rinse and repeat as necessary.