How can I identify the rear end in my E150? It is a 1988 with a 302. Are there troubleshooting procedures available for rear end/wheel vibration?

 

You have an 8.8, gear ratio can be obtained by looking up the axle code on the drivers door pillar or by reading the numbers off the tag hanging off one of the diff bolts.

If you jack up the truck and place the rear axle on stands you should be able to start and run the motor and observer for bent or otherwise non compliant parts. Swapping on another set of tires may also help diagnose a the problem. The driveshaft U-joints can also produce vibration if they are dry, these are not too hard to replace but the shaft has to be removed to do so.