Rear end making hum noise as driving

Gear oil won't make the humming noise, lack of it will. Depending on type of vehicle you're talking about.

1st check center support bearing, and rear wheel bearings

There's not much inside there to see. Beginning at the driveshaf yoke, You have the nut that holds the pinion yoke on, a washer under that, a seal in the housing to keep the lube in, the outer pinion bearing another washer (or spacers, a crush collar and possibly a few more washers, the pinion bearing and the pinion gear itself. The carrier has a bearing on both ends held on to the housing by two end caps. Inside or on the housing you have the ring gear,four pinion gears and a shaft that holds the two free pinion gears in. That shaft has a 5/16 bolt in one end to keep it from sliding out of the carrier. The axles protrude through the two side gears and are retained by two "C" shaped retainers that can be removed only when the cross shaft has been removed. Sounds rather simple but, rebuilding them requires a lot of experience and dial indicators in order to get it right. Reading a gear contact pattern is part art, part science and getting it wrong will result in noise and quick failure. If you have a positraction unit, the posi plates and springs go inside the carrier and are a bit complicated to install without damaging them. There are many end to end differentials you can put under there available cheap from a scrapyard. Only requirement is to get the drum to drum length right and if it's a 4x4 the gear ration must match the one at the other end of the vehicle.On some, you may need to cut the spring mounts off and weld them in the proper places.
If you need info on a specific part inside the rear, ask.

THE LEAK is an axle seal leaking the noise is bearings in rear end could be axle bearing of carrier/pinion bearings while driving shift weight of truck side to side see if noise changes if so it is axle bearing if not then most likely differential bearings

rear wheel bearing.

There are a lot of bearings back there and any of them can make a noise. If you had ground up part all of that ground up metal floating around in the oil can damage all of the bearings. Also, replacing the bearings in the differential is some very precise work and can't be done properly with out following exact specifications and tolerances. In other words you can't guess about bearing pre-load and gear tooth contact. When you take the carrier out, and also change pinion bearings you changed the relationship between the ring and pinion gears (which can also give you a noise) You have got to get a book for this car and follow the procedure and set the gears up to the given specs. You can't just replace the parts. Also, don't forget there is a bearing that supports the outboard end of the axle which can give you a noise too.

Sounds like the gears are not set up right.Ring gear to pinon! if there is too much backlash it will be noisy,and the pinion to the ring gear depth is critacal too.If all the bearing look ok i,d say its a gear problem. Although bearing noise gets worse at higher speed.Do you have a 2 piece drive shaft, with a carrier bearing in the center,it may be rough?

Since you aready paid $400, go back to ;the shop and get your $'S worth!! Unless someone can prove that the axle bgs were bad, you shoulld ask why pinion & side gears were not diagonsed!!! (dosen't anyone test drive stuff after they "fix" something anymore??? Dosen't anyone give a damn???
If you can't get anywhere with this, find a junkyard unit and install it yourself. It isn't that hard. Just be sure that new lone has the same mount points and gear ratio matches ratio lof front axle.(count gear teeth if you must)

It's the wheel bearing. Guaranteed. Just replaced mine. Go to Audiworld tech articles for step by step instructions on how to test the wheel bearings. They must have been put in wrong last time or they just went out again.

Your carrier bearings and possibly the pinion bearings are the source if the noise is a low pitched grumble or gravelly noise that starts just about 20 mph and up. If it is louder when quickly changing lanes to the left, it is probably the right wheel bearing, and if it is louder when changing lanes to the right, it is the left wheel bearing. If it is a whine that is really annoying at 45-65 mph, your ring and pinion are probably worn beyond their design specification limit. If your U-joints are OK, but you can hear a loud clunk from the rear when you get on and off the throttle, you definitely have play in your ring and pinion. Have the cover removed and you can sheck this easily. I have worked on several Jeep Grand Cherokee differentials, and the ring an pinion has needed replacing on them all. A few had bad bearings, too. You should probably replace the bearings and the ring and pinion, because the labor is nearly the same and the parts are just a bit more. If you look through the forums on the www you will find many people that replaced the bearings to fix the grumble, only to finish the job and find out they also have the whine.