Re: '63 Galaxie rear making noise...help!!
It could be a wheel bearing. It could also be a carrier or pinion bearing. Pull the wheels and hubs off. There is a hole in the axle flange to stick a 5/8 or so socket into so you can remove the axle retainer bolts. Pull the axles out, and drop the driveshaft. Then remove all the bolts on the front of the differential. Leave one bolt on the top loose, and break the seal so you can drain the oil out first.
If it has never been out there are little copper washers crushed into the threads that you have to pick and dig at to get off before the third member will come out. You wont need these when putting it back together. Its not going to leak without them.
Be careful when removing the third member, this thing is heavy, so dont let it fall on your head.
Take it and the axles to a machine shop and have them checked out. They should be able to tell you what it needs and do the work. Its probably just a wheel bearing. Also check the u-joints on the driveshaft while you have it out. Pull a cap off and look at the bearings and the post they ride on. If there are marks on it, replace the u-joints as well. The post should be very smooth and have some grease on them.
I love it when people do things right
Unfortunetly I dont always do that lol