Rear diff The rear diff is missing the breather tube and its hole is plugged with mud. Is the truck safe to drive?

remove the rear cover all the bolts except the top 1 just loosen that 1. Put a bucket under the rear diff and open the diff cover and drain out the fluid. clean and reseal the diff. remove the plug on the front of the diff and fill with the correct diff fluid until it is filled up to the hole and replace the plug, clean up and check for leaks. No leake = job is complete.

IF you are in constant 4wd then you will not have a centre diff unless you have an AWD. The difference is that AWD transfer cases have a centre diff that allows different road speeds between the front and rear diffs as in going over speed bumps and dips ion the road It is the same operation in the front and rear diffs that allow one wheel to go faster than the other when cornering. However in 4wd drive there is no diff action in the transfer case and both front and rear axles drive at the same speed regardless of speed bumps and dips in the road . This action produces what is known as torque wind up which results in the handling characteristics. This torque wind up places stress on all the drive line train and results in failures such as .that you describe.. This wind up is not noticeable when driving on loose surfaces slippery surfaces or in mud as it is allowed to escape when the wheels spin . If you have an AWD with diff lock capabilities then check that the diff lock is operating correctly

check the cv joints for wear. check rear drive shaft for worn slip joint splines and "u" joint wear. When you lock in awd there is no centre diff to allow the variations between the wheels and so you are experiencing a torque build up between the front and rear diffs . This put stress on the entire drive chain so any looseness or worn parts will display noises. Remember that the awd lock should be only used on surfaces that allow the tyres to slip and relieve the stress ( dirt road---snow---mud--ice )

diff overheating is from incorrect mesh of the crownwheel and pinion
that can be from too little clearance , too much clearance of failing bearings and too much preload on the pinion bearings
it can also be from incorrect oil level in the diff to the bottom of the threads of the fill plug
it is time to pull the diff and check the bearings
the problem will most likely be the bearing behind the pinion as that one takes all the load
diffs normally run hot but it is the escaping oil that is the problem
that could be from bearings on the pinion allowing the lip of the flange seal to not seal properly

Looks like a hub reduction gear in their but the half shaft has a paper gasket so no problem their ,pair of sissors and a ball bearing to make the holes this is a simple job but when you do this look on top of the diff unit and make sure the breather on the top of the diff unit is clean and not caked up with mud.Then another trick that only us old time truck fleet fitters would do is make sure that you pump some grease into the diff unit LM grease is best ,about half a grease gun full is sufficient as this will get hot and go around inside and deposit on the coolest areas like the pinion seal and down the half shafts stopping a lot of worn seal type leaks ,but make sure the breather is clear whatever you do

Sounds like the rear diff is causing it.

Check rear pinon for it being loose which means the bearing is worn out.
To check it make sure the truck is in park & can't roll then go under the truck to the rear diff and grab the drive shaft close to the rear diff and try to move it up and down, there should not be any play in it. If it does the rear pinon bearing is gone and needs to be replaced before it breaks.

If there is no play it may be internal rear diff problems ..

Note: If you go off roading keep in mind even that your diff's looks sealed but there not and will get mud/water into by the breather tubes causing damage. Make sure all diff's are flushed after off roading.

Hello
This hose goes up next to the air cleaner housing there should be a breather cap on the end of it,,, this is the vent for the frunt axle,,, keeps watter out when your in mud/snow,,,,, if the hose is broke you can go to the parts store and buy a 3 foot chenk of rubber hose run it from the diff housing up to the air cleaner airea,,,, you can use a cpl tystraps to secure the hose to the engine comparmint.
Let me know if i can help more!

If you mean just the raer diff fluid you will have to remove rear diff cover to drain fliud replace gasket reinstall cover and go to access plug at the side of the housing and remove plug with a 3/8 rachet and top off until fluid is just below hole.

Give the old man a pat on the back! There is an oil plug on the rear differential. On a level surface, remove the plug; if oil starts to flow out, the fluid is full. If no oil flows, carefully put your finger in the hole and feel for the oil level. Your finger should go no lower than the first knuckle before you feel oil. If it goes further, you are low on oil and should either fill it up or better yet replace it. Rear axle oil doesn't get replaced nearly often enough in most vehicles and since your truck is 18 years old, would be a bad idea to have it changed. Best of luck.
Greg

To replace the seal you must pull out the carrier assembly and the pinion gear and install a new crush sleeve if you do it by the book, I have found that if the yoke is removed a new seal installed and the yoke tightened to about 50 foot lbs of torque it is ok, as far as the lube goes there is a plug on the cast case of the diff, it will either be a square drive plug or a large allen plug, fill the diff so you can just touch the fluid with your little finger, don't overfill or the axle seals will start leaking.