Unfortunately expats will no longer be able to travel across the border if they have a lean (Loan) on there vehicle. This is a recent law passed this month.

As for your other questions, yes you will need exit permit, yes you will need to apply for transit visa for saudi, and yes you will need a NOC from your sponsor....As for costs, I am not sure since it's been a while since I traveled by road, but the transit visa for Saudi can run you a easy 20-50qr per person, and exit permit is 10qr per person.

Hope that helps.