If my son was test driving a motorcycle but the seller did not ask about insurance and there was an accident in which my son was criticaly injured, who is liable?

The fact that your son did not have insurance does NOT affect liability. 

If your son was not at fault in the accident involving another vehicle, the registered owner of the at-fault vehicle is liable and your son would file a personal injury claim with the insurance carrier of the at-fault party.  The personal injury claim would seek compensation for the medical bills, pain and suffering (an amount in addition to the medical bills) and wage loss.  When your son completes his medical treatment and is released by the doctor or is declared by the doctor to be permanent and stationary, which means having reached a point in treatment where no further improvement is anticipated, obtain the medical bills, medical reports, and documentation of wage loss.  Compensation for the medical bills is straight reimbursement.  The medical reports will document the nature and extent of the injury and will be used to determine compensation for pain and suffering.  Compensation for wage loss is straight reimbursement.  If the case is settled with at-fault party's insurance carrier, NO lawsuit is filed.  If the case is NOT settled with the at-fault party's insurance carrier, your son would flie a lawsuit for negligence against the at-fault party/registered owner of the other vehicle.  If your son is a minor, you will need to be appointed guardian ad litem to file a lawsuit on his behalf.

If your son was at fault in the accident involving another vehicle, he is liable for the accident and the registered owner of the motorcycle is also liable for the accident.  If the registered owner of the motorcycle had insurance, the other driver would file a claim with the registered owner's insurance carrier.

If there wasn't any other vehicle involved in the accident, then your son is liable for the accident and does not have a claim against the seller of the motorcycle.  If the accident occurred on the seller's property, your son would have a claim against the seller based on premises liability and your son would pursue his personal injury claim with the property owner's insurance carrier.  The defense of assumption of the risk could be asserted against your son.  Assumption of the risk means that your son recognized and understood the danger and voluntarily chose to encounter it by riding the motorcycle.  If your son was at fault in the accident, the seller could sue your son for damage to the motorcycle.

The seller would only be liable if he or she was at fault in causing the accident in some way: for example, the accident occured because the motorcycle was not properly maintained (e.g. loose steering, loose wheel, flat tire, etc.); the accident occured because of a  dangerous condition on his property (e.g. a large pothole in his driveway); or the seller otherwise caused the accident in some  way (e.g. he pushed at your son as your son rode past). The seller is not himself your son's insurer, and is not responsible for whether or not your son had insurance. He is only liable to the degree he is at fault.