My question is I have the engine and tranny out of my Camaro and the torque arm off can I drag the car to a car wash to clean the engine compartment before putting my engine back in without hurting the rear end? Thanks for your help.
Clint

Probably if you went really carefully. Is the drive shaft still attached? It will turn. It would be better if you reattached the torque are and tied it in place though. No need to fully tighten it.

put the trans crossmember back in and figure out a way to tie the torque arm to it- ratchet straps, bailing wire, zip ties: whatever you can think of. it's only stupid if it doesn't work.

Yes drive line is out also! Thanks for the info.

Without the torque arm, the diff will want to rotate upward because of the spring pressure pushing down on the back of the diff. Worst case is the springs will fall out and the body will fall onto the diff.

As mentioned above, reinstall the torque arm and find some way to secure it. Even having the torque arm riding on the trans tunnel is better than nothing.

.......

Cleanliness.

It's always better not to have to wallow in 200,000 years of accumulated road and oil leak funk dripping off of everything onto your face while working on your car.

Yes you can load your car onto a roll-back and car-wash it; or, onto a car-hauler trailer, WELL SECURED. Always makes working on one a less unpleasant ordeal.

Yes you can use a tow bar, the same way. Just be sure to take along your floor jack and jack stands.

No you cannot pull it with a jerk strap, rope, etc., unless you have the Saginaw rear discs. Any rear brakes that actually WORK (drums, PBRs) will cause the rear to rotate EXTREMELY and likely either drive the torque arm into the pavement, or break something. The Saggy brakes on the other hand, probably won't do enough braking to make any noticeable difference to anything. Since your car is a 89 and most likely has one of the better (more functional) brake systems, best not to rely on it as the "stopping" member of a tow tandem. Don't try to "pull" it.