How much oil do you put into the differential?

Some tires are noisy.
Some rear axle HD differentials make noise.
Differential bearings may be noisy.
When the differential was drained, the oil should have been inspected for metal residuals.

There are some vehicles that require a special oil. Usually 80 w 90 wieght oil is used in Differentials. I recommend that you drain it first then add oil. Because oil and synthetic oil do not mix. You can call a dealer service department and they can tell you for sure.

The clunking noise is a sign that the rear axle diffential gear oil needs to be changed. Put a catch pan underneath it, and remove all the bolts from the differential cover. Drain the old oil, and spray brake cleaner into the area to flush all dirt deposits from the unit. The brake cleaner evaporates and won't leave a residue.

Put a silicone sealant around the cover before remounting. Refill the unit with the gear oil weight specified in your maintenance manual, and also add a tube of limited slip differential paste (available at Autozone). Fill the differential until it begins to overflow from the fill hole.

Concerning the black gunky substance leaking out: there's a good chance that the axle seal is worn and letting the differential gear oil leak out. You should consider replacing those before refilling the differential. It will continue to leak until you do so.

Best regards,
Steve

II think I would try some Motorcraft XL-3 Friction Modifier. That is what Ford uses to fix the same problem in their Limited Slip differentials. You can find it online or at any parts house that carries Motorcraft.

yes it is leaking differential oil and means that your differential gears are dry and winding becuase rubbing against each other you need buy a differential seal kit and clean off old seal taking apart differential and then put neew on then fill with differential fluid you can use the gasket maker if cant buy a gasket but should be done asap or you will burn up the gears and be left without a vehicle

it really should have the fluid in for safe operation just because they are not engaged doesnt mean no parts are moving inside there will be 2 large fill bolts one low to drain one high to fill the fluid should be just under the bottom of the top hole if its completly empty it will probly take 3-4 quarts to fill

Oil could have been changed and oil additive not used or clutches could be worn out as well.

It should be listed in the owners manual, but because of different oil cooler setups you may have to do the change yourself and add oil until the correct level is established..... for the first oil change.
Most likely 7 liters,but start with 5,run the engine to fill the oil filter,let it sit for 5 mins and recheck and fill to full.
Note the amount needed for next time.

Front Differential Oil Change

1. Before changing or inspecting oil, be sure to stop engine and lift vehicle horizontally.
2. With vehicle lifted up, check leakage. If leakage exists, correct it. NOTE: Whenever vehicle is hoisted for any other service work than oil change, also be sure to check for oil leakage.
3. Remove oil filler plug (2).
4. Remove drain plug (1), and drain old oil.
5. Apply sealant to thread of drain plug (1), and tighten it to specified torque.Tightening torque Differential oil drain plug a: 23 Nm (2.3 kg-m, 17.0 ft. lbs.)
6. Pour new specified oil until oil level reaches bottom of oil filler plug hole (3) as shown in figure. NOTE:

• Hypoid gear oil must be used for differential.
• It is highly recommended to use API GL-5 80W-90 gear oil.

Differential oil specification: API GL-5 (For SAE classification, refer to viscosity chart [A] in figure.)

Differential oil capacity (Reference): 0.9 - 1.1 liters (1.9/1.6 - 2.3/1.9 US/Imp. pt.)

1. Apply sealant to thread of level / filler plug, and then tighten it to specified torque. A: Sealant 99000-31260SUZUKI Bond No.1217G Tightening torque Differential oil level / filler plug b: 23 Nm (2.3 kg-m, 17.0 ft. lbs.)

On the drivers side of the differential, towards the front, there will be a 1" circle, with a sunk in square spot in the center. This is where you put oil in. Use a 3/8" drive socket wrench to unscrew it. (it fits right in the square sunk in spot) WATCH THE KNUCKLES! It hurts if you bang them, trying to loosen the plug. LOL When you get the plug off, stick your finger in the hole, and see if your finger comes out with any oil on it. The oil needs to be filled to the bottom of that hole. When the oil starts coming out of the hole, then you screw the plug back in, and you are done. IF, the rear diff has plenty of oil in it, then you may have another problem, like (inner/outer) bearings.