Normally if you are a full time student and not a resident of a state then you are not required to register and insure you car in the state where you are attending school when you have a permanent address back in your home state. For you son to see about his situation he can contact the Illinois Secretary of State (SOS), the DMV for IL.
According to California Bureau of Automotive Repairs (BAR) section on smog check, since your son and his car are out of state he will not need to get his smog checked to renew his CA registration. The CA BAR states that should not obtain a smog inspection in another state; it will not be valid in California. Unless your vehicle is in Nevada or Mexico, you need not bring it back to California in order to complete your registration.
They say one must simply fill out and sign the DMV's form Statement of Facts (which can be found on the CA DMV site) and then registration tags will be mailed to wherever the car is currently located. If your son has questions about this process the California Department of Motor Vehicles should be able to help him.
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[Let CarInsurance.com help you find affordable auto insurance now.] As for car insurance, your son will have to speak with his insurance company's agent to make sure that they will continue to cover him and his car while he is a full time college student out of state in Illinois. Insurance companies guidelines differ and some will not continue your coverage if your vehicle is out of state for a certain period of time. If his insurance company will not continue his coverage then he may find it easier to register and insure his vehicle in Illinois. | 
