When I accelerate or turn corners from a stop I hear a grinding noise coming from the back of my truck. It is most noticeable when I am making a left turn from a stop but the noise occurs when going straight or turning right too. I am worried that it's coming from my differential but I'm not sure. I have the 7.5 open differential with 3.73 gears so I know it's not the common LSD slipping clutch packs.
I uploaded a video

 

I would check u-joints first but really doesn't read like u-joint issue.

Then I would drain differential and look at the oil that comes out, obviously metal filings would be a bad sign, then pull the cover and have a look at the ring gear.
Rebuilding is not too bad of a job it does require some specific knowledge on shimming for best fit but there are many "how-tos" and videos on that.
Or you can try to find a Ranger axle similar to yours, maybe even with limited slip and swap the whole axle.

Good read here on the 7.5": Ford Ranger/Bronco II 7.5-Inch Axle

If looking at wrecking yards the door tags can help, read here: http://www.therangerstation.com/tech...le_codes.shtml


Long shot would be rear brake issue, there is some play on the axles when turning which can make grinding issue louder on the side with brake drum issue

 

Well I took off the driver's side brake drum and discovered that the hub on the end of the axle shaft (I think that's what it is) ways RR, and its a replacement part. Could this be contributing to my issue?

 

hell to me it almost sound like an exhaust rattle

 

Turns out that's exactly what it was. I moved the exhaust pipe around with my hand and was able to hit the frame with it and it made that metal on metal noise. I zip tied it against my spare tire holder and went around the block, no noise. Came back and cut the zip tie and the noise returned when I went around the block a second time. Turns out it was just hitting the frame. I'm so relieved that it wasn't anything wrong with the drivetrain.

But should I still be worried that the axle shaft of the driver's side is one made for the passenger's side. When my uncle had the truck it got t boned on the rear driver's side and the collision shop must of put the wrong axle shaft on.

 

Well glad you got the noise figured out. Now I'm pretty sure you are alright with the axle shafts and here's why. The passenger shaft should be something like 3 inches shorter than the drivers side. I don't think you would be able to get the c clip on the axle with it being too short. So if you can pull outward on the axle shaft and it doesn't come out you should be good.

 

Good work