Using a free tool such as
www.Seatcounter.com gives you better insight into the actual inventory available. Currently for DL1039 on 4 March, the flight is showing with AT LEAST 9 seats in Coach available for sale. The cheapest fare class of T has 5 seats for sale. Therefore there seems to be plenty of seats and as of now, unlikely for an overbooking situation. To be likely to be oversold, the numbers would be all colored red with 0s across the board.
As to why it may seem that seats are all taken... some seats are reserved for Delta Medallions, partner Elites or those flying on full fare (expensive) tickets. Also, some seats are blocked off, can't be pre-selected and left for assignment at the airport.