I broke my rear axle, apparently it's an old style. Is it easily replaceable?
I have replaced probably three or four axles like yours in the last few months. It is fairly easy; the only special tools that you need are usually cone wrenches (very skinny wrenches to hold the cone-nuts in your hub). The axles are cheap (maybe 10 bucks or so online). You will also need a regular 17 or 16mm box wrench.

Is your axle a quick release (it is hollow inside) or solid? If it is solid, the length does not matter really, as long as it is longer than your old one. If it is quick release, then you have to get it within one mm or so so that the quick release skewer still holds properly. The thread pitch also matters, and is somewhat harder to determine on your own.

I would think that any decent bike shop would be able to tell you exactly what you need. You can order a cone wrench and new axle for probably ~$15 online and do the repairs yourself, and have the original wheel still on your bike.

I'll look around for instructions on how to change out an axle. BTW, this is pretty common for hubs that take freewheels.