As far as I know, you have to pay off the car first, then you get a
lien satisfation from the loan company saying you satisfied the loan.
Then you can sell the car with the title along with the lien
satisfaction note so the new owner can register the car free of no
liens. If you look on your current title, you will notice a lienholder
on it.
You cannot loan your plates to the new owner. The plates belong to you,
not the car.