Rear wheel rubs frame after tire change I recently changed the rear tire and paid no attention to the original working state of the rear derailleur. After a miserable attempt at resembling, I lost what I now think was the Derailleur bolt and nut (one flat side, curved elsewhere) during a short ride. It's since been replaced with whatever nut and screw I could find laying around.

Like the first attempt (with all the original parts still available) at reattaching the wheel, after a hard pedel, especially uphill, the wheel will move from centered. The tire rubs against the frame creating enough resistance to make pedaling feel impossible.  

The rear dropout has a small screw hole and a large triangle cutout. I cannot find a configuration that allows the derailleur to screw into the small hole, and so am fastening it using the larger triangle.

Is the placement of the derailleur the problem? Do I just need to turn the nuts holding the axle on a little harder?

after the axle has slipped down:
You've lost the derailleur hanger mounting nut. Don't worry, they're dead cheap. Without it the hanger won't stay in place without the wheel nuts done up tight. You can get away without one (see matt's answer), but it's not ideal. It's better and less fiddly to use a proper mounting nut:





The way you've set it up now is totally wrong - the triangle-shaped hole is just a cutout in the rear dropout - it isn't designed to have anything mounted to it. I presume the other hole of which you speak is a mudguard or rack mounting eye.