Can you make a claim against an at fault driver without a police report?
yes, but it speeds up the claims process if there was a police report. The claims adjusters for both of your insurance companies will investigate.
If a truck driver sideswipes your car while going down the road and you don't call the law but you have his information what can you do about it?
If someone takes your car without permission and returns with dent in door what are your legal rights?
In order to collect on your insurance you need to report the unauthorized use to the police and obtain a police report to send to your insurance company. It sounds as though you know the driver since the car was returned to you. You would also need to identify the driver. On the other hand, you could sue the driver in small claims court.