Are there threads on the hub on the side without the sprocket, just outboard of the flange that holds the spokes, opposite where the sprocket is in picture #2?
It looks like you have a singlespeed wheel that's been respaced for a wider frame. The best solution would be to remove the spacers and either buy a new axle or shorten the old one. Generally speaking, making an axle wider by adding spacers without getting a wider hub weakens the axle a bit; plus, there's no art or skill involved provided you can do a fairly good job cutting through the axle with a hacksaw, unlike cold setting a frame.
You just have to make sure the rim remains centered. Assuming the person who respaced the wheel did a good job, you simply have to remove the same thickness of spacers from the right and the left. However, I would check. Put the wheel in the frame (or just lay it on top of an upturned frame, and see to it that the hub protrudes evenly from both sides), then see if the middle of the rim lines up with the rear brake's bolt or the hole in the frame for it, if it's removed.
The axle is the threaded stub sticking out of both ends of the hub. The locknuts are holding the spacers against the cone nuts. If you remove the locknuts from each end of the hub, the spacers will slip off. They are the little cylinders just inboard of the outermost nuts.
The locknuts also serve to hold the cone nuts in precise adjustment because they are what the ball bearings run on. If you fiddle with the locknuts, you have to find a source which will tell you how to set the cone adjustment. There's advice on this forum or on various cycling sites or books.