Thanks for all of the hints. I was able to reattach the wheel to the axle. Here is a photo of the wheel and axle. There was some knurling on the axle but not enough to grab.
I got some Loctite (the removable kind, in case I messed up). I used a large pair of channel locks to rough up the axle.
A close up of the axle after applying the pliers and a few drops of Loctite.
Here is the wheel reattached. It's on solid.