Well, this sentence is gramatically correct, but it just doesn't sound right.
It's more natural to say "Many soldiers died in the war" (Talking about a war that already ended) or "Many soldiers have died in the war" (Talking about a war that takes place right now and hasn't ended yet).
If you want to use the word "were", you can say "Many soldiers were killed in the war" turning it into a passive form of a different verb.
I hope this helps. =)