The World Wildlife Fund defines 8 distinct terrestrial ecoregions in Iraq ranging from the Eastern Mediterranean Conifer/Broadleaf forest in the north near Turkey to the Persian Gulf Desert in the South. Take a look at the Map on the National Geographic site.
Here's the 8 Regions and Links to their respective pages which contain lots of good information on the wildlife and vegetation of each area.
PA(Palearctic)0446 - Zagros Mountains Forest Steppe
PA0812 - Middle East Steppe
PA0906 - Tigris-Euphrates Alluvial Salt Marsh
PA1207 - Eastern Mediterranean Conifer/Sclerophyllous Broadleaf Forest
PA1303 - Arabian Desert and East Sahero-Arabian Xeric Shrubland
PA1320 - Mesopotamian Shrub Desert
PA1323 - Persian Gulf Desert and Semi-Desert
PA1328 - South Iran Nubo-Sindian Desert and Semi-Desert
I found a few more bird pictures from soldiers. These pictures are of a White-winged Black Tern on the Tigris River in Baghdad. These birds are a common sight on both the Tigris and Euphrates Rivers during the summer. They nest in marshes and wetlands along the river as do Whiskered Terns which were also common where I was near Balad.
Also here's a story about Barn Owls living at LSA Anaconda in one of the bunkers. I saw a pair of barn owls on Anaconda a number of times and I heard of reports from other bases. They seemed to be fairly common. The subspecies in the region is Tyto alba erlangeri. On Anaconda a little owl was also using a concrete bunker for a roosting site.