Ouch! the desks are nailed down?
As far as breaking them up, you can just number them. Go down the isles and call out a number (1 through 6 or however many number of groups you want.) Touch the kids on the shoulder or something as you number them. Touching them lets them know who you're talking to and that they need to remember that number.
Once you've finished just designate where in the room you'd like the 1s to go and the 2s, 3s, 4s... ready set go! the race begins.
You can do pretty much any activity once you're in small groups. If the game is complicated just use one group as the model while to other groups watch. Then, break up.
You can also start activities without every group really understanding. Once the other groups hve started then you can go around and help the needy.
Also, sometimes the kids will come up with better games than what you had explained. As long as they're using the English, who cares!