We walk where nutria are living and my dog loves to eat their scat when she finds it. Can this give her a disease ?
We would do best consulting a veterinarian on the disease possibilities from the scat. Although I lack data on specific internal parasites of nutria in Oregon, I do know that in other parts of the country humans (and I suspect their pets as well) CAN contract roundworms from contact with the animals and their scats.
I would recommend limiting your dog's ingestion of the scat, if possible. If it isn't possible, letting your vet know would probably be a good idea in case they want to screen your dog for additional worm species when you take him/her in for annual checkup and shots.