Once the rear wheel, brake caliper and brake rotor are removed, the nature of the leak is easier to see. The rear parking brake shoes are also contaminated with oil and will have to be replaced.
Removing the axle shaft shows the actual problem. This axle shaft is badly grooved from a worn bearing and causing the leakage.
The right side axle seal is also leaking, to a much lesser degree.
While bad axle seals allow oil to leak out, they can also allow water to leak in. This can be a far worse problem. The milky colored oil in this differential indicates water contamination of the lubricant.
The ring gear has been damaged by corrosion and is the source of noise in this differential. These gears will need to be replaced, at considerable cost.
Water also often enters a differential through a damaged vent tube. In this instance this is not the case as the vent tube is still fully intact. Driving though water, above the height of the axle can allow it to enter the differential. This is particularly bad if the axle seal is leaking.
Best is to avoid driving though high water and have leaking seals addressed immediately. Professionals like AGCO Automotive can spot and often prevent more serious damage. Properly servicing this differential might have prevented an expensive rebuild, replacing the ring and pinion gears. Avoiding repairs rather than simply repairing damage, that's the AGCO way.
