my LBS mechanic and I were talking about my squeaky bikes a while ago. He mentioned there is a rubber seal (more like a big rubber cup (or cone?) ) on the non-drive side of the rear wheel (outside of the hub, not internal or anything) . He said he's seen bikes squeak at this seal a few times, and just applies a bit of grease to the seal where it rubs the hub. I think it usually spins with the hub, so you may need to apply grease on the axle as well (if you have this seal).
I think it's only newer, cheaper wheels which have this big rubber cup. If you've got a nice old bike, it'll just have more of an integrated washer kind of seal.

This makes sense to me since were walking your bike. Not a lot of stuff to make noise except the wheel hubs.
Maybe time to re-pack the hubs? All you need is water proof grease, a set of cone wrenches, Overhauling & Repacking Hubs , and the gentle touch to make sure you leave the "right" amount of play in the hubs after everything is back together. I like the heavy duty blue shop towels for this job too.

I bet you could get a 99-page thread going on what is the "right" amount of play to have.....