Am I still responsible for paying for a repoed car that I no longer have? If not how do I handle it.

Yes what they do at least in my state is resell it and take highest offer, you still must pay the difference of what is still owing after the resale.
It is normally an auction they hold

Yes it happens sometimes after they repo the car, they add repo fees, and then sell the car. Normally at auction and then normally for a lot less.

So basically after the sell the car you owe them the balance of your account.

You signed a contract to borrow x amount of dollars and to pay it back. If you default on that contract, the lender has a right to repossess secured assets and dispose of them. If the value of those assets do not cover the outstanding balanace, then you are still responsible for the difference.