Are you supposed to avoid overdrive when towing a trailer with an automatic transmission?

You got it right, never use overdrive when towing. If you are driving an automatic or standard, never use overdrive when towing. Ok so you ask why? Overdrive units have a set of planitary gears that arn't built to take the abuise or load placed on them when towing, over a period of time, sometimes a short period, the planitary gears will go out. Hello shop.

Yes!

The transmission take a real beating when the torque converter gets locked (overdrive). Short life$$$$$$

yes. the engine produces more power at higher RPM's so if you were cruzing on the highway, and the engine was running to slow, it would be too much work for it.

Yeap!

avoid using od until you get up to speed...once you are up to speed then it's ok to let it shift into od. keep in mind when you get into traffic or have to stop...shift out of od until you are back up to speed again.