What is causing a humming noise in the rear of the car an how much would it cost to repair

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

Possible wheel bearing getting noisy. Most automotive repair shops will have a technician test drive the vehicle free of charge. A wheel bearing noise can be easily identified by a well trained tech

unlikely--- humming noise is from a vibration caused by failing drive line joints , bearing failures, out of balance drive shafts , failing rear engine mounts, worn slip joints, worn output shaft bush in the transmission housing
it can also be from bad tyres or tyres with a regular tyre pattern in the tread
To understand this you have to closely inspect the tread pattern of tyres and you will see that the pattern is not consistent around the tyre as that consistency is what gives a noise ( example is the old bar tread tyre and the road hum that was produced on hard surface roads)

Unfortunately, this is a somewhat common problem. Ford has issued several Technical Service Bulletins related to rear end noise. Without an extended warranty, this is something you will have to pay for.
TSB 05-23-3 11/28/05 REAR AXLE NOISE REPAIR FORD: 1997-2005 Expedition, F-150 2002-2005 Explorer LINCOLN: 1998-2005 Navigator 2003-2005 Aviator MERCURY: 2002-2005 Mountaineer
ISSUE:
Some vehicles may exhibit an axle whine or hum during acceleration, deceleration and/or cruise.
ACTION: An axle repair kit has been developed which incorporates most parts required for a comprehensive axle repair. The kit should be used instead of installing a complete axle assembly to repair an axle whine/hum. Replace Ring and Pinion with Axle Kit and Components.

for the humming check the rear tires for uneven wear. if the are choppy that will couse a humming noise. next check the axle seals, if they leak the rear diff will run low on fluid and cause the bearings to make noise. if the seals are leaking the rear diff will have to come out and be inspectec for internal damge,last possability is the rear wheel bearings they can be checked by raising the vehicle and moving the tire in and out to see if there is slack if there is movement from in and out they will need replacement, the have to be pressed in so you might want a shop to do that repair

I had a similar issue and it ended up being a broken wheel bearing. I even ended up having two, one was broken on my front passenger side, and one broken on my rear driver side. The part costs about $280.00, but could cost around $400.00 with service repair. The noise of a broken wheel bearing can sound like a humming, and over time it becomes louder. The car can be driven with a broken wheel bearing, but doing so can eventually lead to other wheel/tire maintenance. MINI's endure this commonly due to their low profile to the ground. Here is a forum on further issues experienced, including the bearing, and efforts towards recalls. http://newmini.wordpress.com/2009/02/17/mini-cooper-power-steering-failure/#comment-884

hi this sounds like your brake pads have worn, or the brake shoes as well, if you have drum brakes on the back it will be shoes, if disk brakes will be pads+shoes (inside the disk) if it was the wheel bearing you would hear a loud humming noise not rubbing noise, is it a metallic rubbing noise or a rubber squeaking rubbing noise? just check condition of tyre on back if it is the squeaking rubber noise cost will depend on where you take it and if you do it yourself, possibly $40 to $50 at a garage/auto shop or possibly $20 to $30 if you do it yourself, this just depends ...hope this helps

here is a list of things that cause humming from the rear busted belt on the tire, bad bearing/s on the axle/s, planetary gears, dry rear end ring and pinion gear

from your symptoms of noise from rear ? i would say your suspision is correct it is probably one of hub bearings in the early stage of wear/burning out front wheels chocked raise each rear wheel in turn and with park brake off check for undue movement /rock in wheel/s and any noise when you spin ? if oone shows to be suspect ? advise you replace both sides ? this is not too expensive a repair and can be diy if you have tools and confidence? bearings come as a kit for each wheel/hub if you have time you will save $$$$$ in garage cost? hope this helps/inspires you best wishes from uk

Wheel bearing is the most likely cause. Prob a 1.5-2 hour labor rate job in the shop.