Unless you are removing the cover (catching the gear oil) and inspecting the oil and inside the housing, sticking something in the fill hole just is not going to cut it! A chunk of metal will sink to the bottom!
Do the easy stuff first (like checking the universal joints).
I looked at a truck for a lady once. It was said by a shop to need a transmission, maybe even a transfer case. They did not dig real deep, they just drove it and gave their opinion to her.
I drove it and it started making a racket at about thirty five mph. Sounded real bad. I crawled under it so see if anything was leaking or obviously torn up (I am not much on automatic transmissions)
I looked around pretty good. Made my way back towards the rear axle. There above my head was a small black shopping bag (a gallon of milk would not have fit into it) snagged on something. Upon removal and another test drive, I told her I had fixed the transmission and transfer case. LOL!
Not wanting to get you all excited with that story, But it can be "Not so serious".
Check the joints, do it right. I hope you understand my pictures.
Other stuff could be wrong, eliminate the easy and obvious stuff first.
While you are under there.
Your rear axle tends to/tries to 'nose up' while torquing under power while moving forward, letting off the gas it tends to drop (maybe not much, I am speaking of the middle where the drive shaft connects on). Look for things that might contact the driveshaft when it noses up. A plastic shield scuffed up/ something metal with a shiney spot/ even road kill wedged in there.
A common good joke that used to be played on people was to get one of those big heavy nylon zip ties and zip it onto the victims driveshaft. This might quickly be caught onto as it slapped the underside of the car. I have seen it go on days and days while the victim thought his vehicle was about to bite the dust. Usually it did not take long for the zip tie to beat the long tail off and the noise would cease.
I cannot imagine what kind of immature person might do such a stunt to a fellow human being. LOL!
Images (Click to enlarge)
Thursday, November 24th, 2016 AT 7:04 PM