What's your home unit? Do you have anyone living around an AMC base? If so, you can have them give targets to USO and they can fwd by MIL Airlift to a POC at your base in Iraq.
OR
Directly contact companies..I know you will run into shipping issues this way...so Upfront tell them to ship to APO AE...if they can..problem solved...did this with icy-pops for guys working C-130s in 130 deg. desert heat...they sent me 10 cases 100 each...gota love companies supporting US forces!!
If you need help...I leave S. Korea end of Oct and be at Dover AFB, DE in Dec...after taking all Nov off to bow hunt/family time....add me to friends list....I am C-5 aircraft maintenance supervisor...I can throw a box on jet cuz they are MY jets and i know where they are going cuz it MY flying schedule...let me know n keep safe!