This set is in a Stevens Walden OD box and probably made for the military.  However, I have never seen such sockets before.  The set has a standard Walden 1/2" breaker bar, a 3/8" Walden sliding bar and a Stevens Walden 3/8" to 1/4" adapter.  These are all needed to fit the sockets I will now describe.  Starting from the left 1. 1/2 drive 5/8 hex with a 7/16 hole in the center.  2. 1/2 drive 9/16 hex with a 3/8 hole in the center. 3 & 4 1/2 drive and 1/2 and 3/8 hex no hole.  5 & 6 3/8 drive with 5/16 and 1/4 hex ho hole.  7, 8, 9 and 10 are all 1/4 drive  and sized 7/32, 3/16, 5/32 and 1/8 and no holes.  Anyone have any idea what it have been made to service.

Allen Head Socket Screws?