Looks like tubular rims to me. Most of the discolouration will be glue and not rust.
- Hot air gun - a hairdryer might work but they don't put out as much heat
- Wooden popsicle sticks, with a rounded end.
- Wheel truing fixture OR an old fork in a bench vise OR the bike's frame.
- Glove for heat protection, or rags to protect your hand
- More rags/paper towels to wipe up glue waste
Mount your wheel so it spins freely. Use the hot air gun to soften an area of glue between two spoke holes. Play the hot air around and don't focus in one area. Try and pre-warm the next sector upward too (heat rises)
The glue will soften and then you can scratch the bulk of it off using the wooden sticks. The last bits can be wiped up with the rag.
Be careful, the glue will be over 100 degrees C and will burn you.
The glue is somewhat wet too, so it may run, it will soak into cloth, and it will adhere to skin continuing to burn.
The rim will also be hot, and this heat could damage stickers/decals.
Work quickly, and be prepared to do multiple laps of the whole wheel. You don't have to get it perfect either - 95% clean is good enough.
When refitting the new tubular tyre, its personal preference if you want to use tubular glue or tape. Both are messy, tape somewhat less so.
Remember glue-up takes a while - do it properly and you'll have a well-bonded tyre. Expect to take a couple days for a complete cured tyre.
I really like riding on tubulars, but they're such a faff and a puncture en-route is often ride-ending. As such clinchers are more practical. So I save my tubular wheels for the annual Merckx time trial on my `80s road bike, along with the wool jersey and leather shoes.
Are those steel or aluminum? Are they worth much to you or on the market?
This probably isn't the most professional answer, but I recently got some old steel rims that were covered in surface rust. I used a steel brush attachment for a battery-powered drill, I doused the rims in rust remover (hydrochloric and phosphoric acid), and when the material was clean enough of rust to my liking, I sprayed on 2-3 layers of spray-paint clearcoat to prevent further major outbursts of rust.
Obviously this scratched the wheels, but they aren't worth much and I just needed a fix good enough to be able to ride the bike without worrying about rust eating through my tubes and tyres.
If your rims are aluminum then this advice does not apply (aluminum does not rust). Likewise you wouldn't want to scratch up a rare and expensive wheelset with an iron brush.
NB. If what we're looking at is just glue from old tubular tires, you might have luck with various solvents. WD-40, paint thinner, etc. have all done the trick for various glues in my experience, without damaging the underlying material.