Two Turkish ones: "Canakkale icinde" (about Gallipoli) and "Burasi Mustur" (or "Havada Bulut Yok") about the Mesopotamian front. Lots of YouTube videos of both; they are both traditional with no known composer, from the time of the war itself.

The nation that suffered the most casualties in WW1 was Russia. Next was Francophone Africa, then the Austro-Hungarian Empire. How about some songs from those places?