Your situation is unique, so our advice may be limited. Each state has individual laws regarding how long a vehicle can remain without being registered or insured. In Oregon you can normally only register a car if you are a resident of the state. But according to the OR DMV site, a vehicle may qualify for Oregon registration even if the owner is not a resident of Oregon if it fits certain situations.

One situation listed is if the vehicle is left in Oregon when the owner is away from Oregon, is primarily for personal transportation in Oregon and is a private passenger vehicle. So under this you might be able to register and insure the car while it stays at your parent's house in OR.

If your grandfather is willing, another option might be for you or him to contact his insurance company and ask if you can be covered to borrow his car and drive it out of state (to Oregon) where it will remain for 2 months on his policy and coverage. Also, verify that you will have coverage on his policy while you are driving from Oregon to California and taking possession of the vehicle.

If your grandfather's insurance company is willing to cover you for this time period you can wait until you get to California to register and insure the vehicle. You will want to contact the Oregon DMV to make sure you comply with their requirements while in OR though.

If you are unable to have coverage through your grandfather's policy, try contacting the Oregon DMV to obtain temporary registration and contact a carrier in Oregon to get coverage while the vehicle will be in Oregon or in transit to Oregon. Then when you move from Oregon to California, you will need to follow that same procedure in CA.