Where can I go to find out what which rear axle I have and the gear ratio

 

There are 3 ways:

First, is a sticker in the glove box (if its still there)
Second, is request a build sheet from the dealer or Dodge.com (you will need your VIN)
and finally, craw under and look at the cover. There should be a metal tag bolted to the bolts that hold on the cover. It will say either 3.5 or 3.9... 3.5= 3.55 and 3.9= 3.92.

To check for limited Slip:

 

Enter your VIN on this page - https://dodgeforum.com/forum/vindecoder.php - then click on the "Equipment" tab.

 

The sticker still there but doesn't have any axle info. Haven't done the second option. C568 where the only things that was stamped tag on the rear axle. I was able to get the gear ratio,The original owner kept the window sticker with the price and vehicle infor with owners manual. I'm curious on the vin #. Used the vin decoder, it states that the transfer case is the NV 231. The NV 242 is the one I have. Also on the rear axle it had both 3.55 and 3.92 ratio.

 

You should not have different ratio from front to back, that is very bad and means someone who didn't know what they were doing replaced either the front or rear with the wrong gears or axle assembly. Since you do not have the transfer case specified by the vin I would say someone has done a little work on the drivetrain. If you are having trouble with the gears which I assume you are since you are here it is probably because of the mismatched axles. The transfer case you say you have is AWD and with gear ratios that don't match cause transfer case bind. Sometimes I have seen the gear ratio also written on the side of the gear set inside the differential also.

 

you can also jack up the rear end w/ the car in nuetral and count how many times the driveshaft spins for one turn of the tire . . . takes two people but should get ya your answer ~3.5 turns and you have a 3.55 just under ~4 and you have 3.92s . . .

 

Thanks to everyone with the suggestions. I was able to the gear ratio's and a little by more. Going through all the paper work that comes with the owners . Apparently the original owner kept the display sticker that shows the price and vehicle info. It came with a few options.
Has 3.92 gears
. The NV242 full time full time transfer case
The 4 wheel anti lock
There's few more as well. Just wanted to let you all what I was able to