Diminished Value Insurance Claim or GAP lawsuit.

No, if the car is totalled, you can NOT sue for what you still owe on it: when a car is totalled (or any property destroyed, for that matter), the at-fault driver is only liable for the then-current value--the fair market or blue book value--of the vehicle. What you owe is irrelevant and the law ignores it since this varies so much: some people buy for cash and get a better deal, some finance and get a worse one; some are good negotiators, others bad; some have a trade-in to reduce what they have to pay, others don't; some people are given a car as a gift, others are not; etc. The only relatively consistent & fair measure is value, so that's what the courts use. (And this is why if you finance a car, you should purchase GAP insurance to protect you.) 
If the car is repairable, you can potentially sue for diminished value IF you sell it and the buyer offers you less than it "should" be worth based on what it's "blue book" value should be at the time you sell it. You can't sue for diminished value unless and until you sell the car, since until that happens, there is no loss--i.e. you only lose money (and can only determine what that loss might be) if and when you sell the car. That is because the law deals in actual losses, not theoretical ones.
(Example: say the accident makes the car be worth only 75% of what it might be. Say that right now, based on age, make, model, etc., it should worth $20k, but you can only sell it for $15k--you have a $5k claim potentially. Say instead you wait 8 years to sell it, when it might be worth $8k, but you sell it for $6k--your claim is only $2k. And if you never sell it, you suffered no loss. So the existence and extent of any loss is only known if and when you sell.)