if you think it is the differential, you can pull the plug and drain the oil. The diff plug usually has a magnet on it and you can see if there are any pieces of metal. before you pull the drain plug, make sure you can break the bolt used to fill the diff with oil.
if the noise is a grumbling sound that happens once you get some speed and then let off the accelerator, the first thing I would check are the driveshaft u joints. When was the last time they were greased?
If the noise happens when you turn, try to listen to what side it is coming from, as it is most likely a hub bearing.
if all that fails, you can check to see if the backlash of the diff is excessively loose or tight by jacking up the wheels and moving side to side. Not very scientific, and you'd probably already know if it was that bad. the pinion in the diff can be checked if it is loose by taking off the drive shaft, grabbing the flange and pushing/pulling on it, there should be no movement.
I'd start with driveshaft u joints, then hub bearings.