It looks like Brian lost the thread here. : )
Speedo cables do sometimes get stuck in the drive unit or speedo. Some drive units are designed to work in either direction and have two ends into which you can put the cable. If yours is this type, there will be a plastic cap on the drive unit in line with where the cable goes in. If you have this, remove the cap and see if you can tap the cable out with a pin punch.
If it is not, dis-assemble it as Brian sugested and see if there is a circlip or something similar holding the drive worm in place. You may be able to remove the worm and get a punch in the other end of it.
As for the wheel nut, make sure none of the exposed threads are screwed up, then remove the nut.
If you do strip it, either buy an axle or have a local shop cut a size smaller thread.
Sooner or later, you will have to adjust the chain or risk a rear wheel lock up.
When you replace the wheel, be gentle with the wheel nuts.