How can I get orders for 2 of my deployments to Iraq (1-319 FA Aug03-Mar04 and 2-3 FA Jan06-Feb07)?

I have used https://mobcop.army.mil/MobcopPortal/UI/Login.aspx

Stipulating that I left the army in 1996 and that my answer is low-tech, have you requested a copy of your official DA microfiche? It will probably be there.

Anything prior to 2009 most likely won't be on MOBCOP due to them being automated after that point and any hard copies are no longer on file .....you'll probably have to contact battle buddies that you deployed with or contact the issuing agency for the orders.