We hauled a lot in, as well as helicopters, hangars, UAV's, weapons, and a host of other things. If it's available in-theater, it has usually been flown in.
I rather doubt it was "tens of thousands". If you could load 20 per 744, it'd be 500 flights to move 10,000. And 20 per plane might be high.
About twenty five thousand went to Iraq and Afghanistan. In the Afghan theater, most of what came in arrived by air. This was especially true when the Pakistanis closed the borders.