In Rear corner of backyard there is a 2 foot wide by 3 foot deep hole.
This is probably caused by drainage to the lowest part of the yard as it slopes that way. What is a good temporary fix until next spring or later? What kind of kind of fill is appropriate and how should it be layered?

e.g. large stones, gravel, quarry dust, dirt, sand etc

Doesn't sound good to me. I would avoid large rocks and anything else likely to be hard to remove. I would go with the dirt or quarry dust. Holes don't develop just from water draining. It could be washing the dirt into an old broken drain. If you have limestone in the area, it could be a natural sink. Either way, it will never stay filled. A drain could be filled, but I will leave a natural sink to somebody with successful experience with them.

If this is in the rear corner of your yard and not a safety hazard, let it stay the way it is until spring and you may find out if it will get any worse or not. I had an old rotten tree stump in my yard that I didn't know was there and as it deteriorated the ground sunk. When I found out what the problem was by digging down, I filled the depression with good soil, planted seed, and it has been ten years since then with no further sinking. Whatever you decide, remember that it is easier to remove soil than anything else you could think of putting in there. Try digging down a bit if it continues to sink and you might get a look at the problem.