The humming is likely (also) the rear diff. Change the oil to 85-140. I prefer Amsoil as most now. You can also try their 190 race oil. That WILL dampen noise

Vibration is most likely the prop shaft. Put a straight edge on it. Remove the shaft and check CV's and center bearing. Be sure it's aligned during installation. They are usually crooked and/or the spacers are missing (corrects for up/down).

Unlikely the cheap axle. The bearings do tend to get a bit loose moreso than OE. Haven't seen any issues on a few cars so far including my own.