What is the technical name for this nut-bolt thing with inner hubs?
They called cap nuts, and often the washers will have an anti-rotation tab on them that is bent in so it slots into the dropout. They have an oval hole in them to lock onto the flats on the axle.

If you're lucky the thread is an M10 fine (M10x0.1mm) and an industrial fastener outlet will have them (I use www.bolt.com.au), but there are a few fairly common sizes around so it would pay to make sure. If you are working on older bikes and buying tools a small thread pitch gauge would be a useful thing to have, they're under $20 here. But trying to measure the thread inside a cap nut with one is very hard work and youŕe likely to get it wrong. The better alternative is to buy an axle thread set - basically a short section of each of the common threads on a backing plate. You try the axle or nut you have on each until you find the one that it fits (the tool is clearly labeled).

From your torque question and the pic above, I suspect you are trying to do up the nuts to stop the wheel sliding forward in the dropout. For that you need serrated washers that cut into the dropout. And damage it. The better option is a chain tug as previously discussed here. A torgue wrench won help much with old nuts and axles, as they tend to lose strength as they wear.

Edit after the new photos: The Shimano anti-rotation washers are nice and thick, also serrated, so need to go on the outside of the frame (where they are now). You've already done enough damage to the dropouts by digging things into them. So you need a thin chain tug to fit inside between frame and hub. Also one that you can file off any protruding aligning bits, since your dropout opens forward rather than backward. I would look for one that has two screws rather than one, so it will be more stable on that curve at the back of the dropout. I have one like that on my commuter.

 or at least an outline of where it should go - obviously behind the frame rather than in front of it as sketched.