There are multiple companies that can help with that. Most of them are international companies known for helping with such tasks. Few others are Regional that can also handle shipping form the US to Iraq.
As far as specific companies, I would suggest either Agility agility.com/EN/Pages/Default.aspx
Or you can go with MoveOne moveoneinc.com
The rates would not be cheap but the service would be good. Another option would be going online and searching for shipping companies out of UAE. There are hundreds of them who can take your items from anywhere in the US and deliver to anywhere in Iraq.
Should you need further help, message me directly and I will be glad to help you.
