Looks to be an Eaton HO52 axle, which has full floating hubs/axles. The silvery look to the oil you drained may be swarf from failing bearings or gears. If you saved the oil put a magnet in it and see if anything sticks. I can't be sure from the photo but it appears that there are some pits on the gear facing. Look closely. Get some hi-spot blue and paint some gear teeth to see what sort of pattern you get. If the pattern is OK it probably won't howl. While the cover's off check the differential gears for slop and obvious wear. Washboard roads will do these in after a while. Take your dial indicator and check the ring gear backlash against spec. Then you can pull the carrier bearing caps and have a look. Then pull the pinion, replace the seal and have a look at the pinion bearings. If you have to replace the front pinion bearing, start looking for another axle or pumpkin. That bearing is well over $500 last time I checked. If everything's OK reassemble with new seal and pinion gasket, set the backlash to whatever it was before and put the back cover back on. Usually, these axles are tough as an old boot and rarely give trouble.

1951 3800 1-ton
"Earning its keep from the get-go"
In the DITY Gallery
1962 261 (w/cam, Fenton headers, 2 carbs, MSD ign.), SM420 & Brown-Lipe 6231A 3spd aux. trans, stock axles & brakes. Owned since 1971.