We are told we must clock out on time--no overtime allowed--but that all the work must be done before leaving.
This is a violation of the Fair Labor Standards Act. Contact your local Wage and Hour board and turn them in.

If we got injured at that time, we wouldn't get any compensation would we?
You are correct. It's up to you to prove that you were injured while performing your regular job duties. If you are injured while working off the clock, there is no record of you performing those duties, and it becomes your word against your employer's.