Anyone know what these are used for? The nut is one of those with the wedge-shaped 'washer' portion.

I should have put something in for size reference. The ring with the 4 tabs is about the size of a quarter.

Not sure what you are working on, or if they are misc. parts you have there but I'll give it a try, but I'm going off of what I've seen on A-bodies.
I believe the sheet metal nut(bottom right)is a retainer for a remote mirror knob. The "ring with the 4 tabs" looks like a window regulator roller retainer. To the left of that looks like rubber glove box door bumpers. Flange nut, have a couple in my parts bins, but I can't think of where they go right now. And you're right they aren't like a regular flange nut, the flanged area is indeed wedge shaped. Same with those 3 funky looking sheet metal nuts to left. I know I've seen them before, but can't place them right now. To the left of the flange nut at the bottom, looks like the retainer for the pin that holds the e-brake handle to the dash (A-body). If you think that's what it might be, I can get you a picture to show where it goes. The roll pins might also be for an e-brake handle as well, as there are 2. One to attach the plastic handle to the hollow rod and one in the other end of the rod that catches the pivot spring. That U shaped thing in the top right, is that a sheet metal clip? Again, I know I've seen it before, and now it's going to bug me until I figure it out. That's the best I can do for now, and I might be way off. Maybe someone else can throw in here.

It would help if you could say what car you think they belong to. My expertise is limited to just one restoration, a 69 Barracuda 340-S.

1. Two rolled pins at upper left: 2 pcs 3/16" dia x 1" L are used in the exterior door handles return assemblies. One pc same size connects parking brake tube to lever. Another pc 3/16" dia x 13/16" L connects parking brake handle to tube.

2. Rubber bumpers: Looks like the 2 bumpers in the dash panel that the glove compartment door closes on. These fit a 1/4" hole.

3. Retainer with 4 tabs in the ID: Retains quarter window plastic rollers.

4. Stamped nut in lower R corner: If 3/4"-10 threads and 1 1/8" across flats, could be the manual transmission reverse indicator light retainer in the instrument panel. Or some similar I.P. app due to good condition.

5. Rusty nut, lower center: If this is a one-piece locking hex flange nut, and if 3/8-16 thd, could be for muffler clamp. If 5/16-18 thd, could be for park brake cable adjuster rod, or wiper motor to firewall, or manual transmission floor shift lever.

6. Spring nut, push type, lower L center w 8 ID slits: If for 3/16" stud and 0.44" O.D., likely retains one of the control cable ends that attaches to a lever, switch, or door in the heater or A/C box.

So sorry. Yes, I neglected to mention what these are from. These should all be from 1970-1974 Barracudas, and the quantity shown does not necessarily reflect the quantity used per car. These are a collection from likely several cars.

The U-shaped clip is metal.

The rusty nut is one of those somewhat funny shaped ones. At one time I was thinking it was for the radiator shroud. Not sure.

Thanks.

The three cup shaped nuts on the left could be for a console cover. The cover comes in two pieces and I believe those are the style of nut on the plastic columns inside that the screws go into to hold the inner half to the outer.

I'm no expert on E-bodies, but I recognize a few of those items from A & B cars:
U-shaped clip holds headliner to body flange
Nut with wedge-shaped (or cone-shaped) washer, machine thread for trim such as '68 RR trunk Decor panel
Stamped nuts at left also used on Duster sharktooth grilles
Window-roller clip & bumpers as previously identified
Roll pins always seem to go where they're a PITA to deal with
Shallow (stamped?) nut bottom right could be for accy lamp or even radio depending on size/thread

The big flat nut could be for the remote mirror control.

Restoration Specialties & Supply Inc. can identify these for you as well as supply these to you. I just found them and I am amazed at what the stock. Send the pic to them.

Topside, you reminded me that the 3 'nuts' on the left are for the ends of plastic pegs, as I recall, like on the back of some interior parts, and also possibly for some grill related stuff.

The U-shaped clip is larger than the headliner clips.