I live in Oregon and my 17 yr. old son is planning on getting his driver's permit this week. His dad has sole custody (both legal and physical.) Before dropping my son off at his dad's yesterday, I told him to make sure his dad's car is registered before he begins driving. He wondered how I knew it wasn't registered and I told him that I could see by the tags on the license plates.

After speaking with DMV and local law enforcement this morning, I'm really concerned about potential liability for both my son and myself. If my son was involved in an accident while driving an unregistered/uninsured car, who would be legally and financially liable? Law enforcement told me it would be my son, since it's the driver's responsibility to confirm the vehicle he's driving is registered and insured.

I don't know whether my ex has considered how this could affect our son's future. Our son would more than likely lose his ability to get his license and will also be stuck with an SR-22 filing on his DMV record (certificate of insurance required for 3 years), not to mention, outrageous insurance rates.

Worst case would have course be injury/death. My question is only relating to legal and financial liability. My health insurance would cover any injuries my son might sustain.
If there were injuries sustained by another party, could that party sue me - the NCP if they can't get anything from the CP (Dad)?

You would have no liability as you are not the custodial parent. And it is not your vehicle.

You can only push a horse so far but you can't make him drink. If dad does not get vehicle properly registered, licensed and carry insurance on it - this is NOT your responsibility. Someone has to learn to grow up and get this vehicle "legal" and get insurance on it. You won't be getting the ticket - someone else will.