We were part of an eradication effort, so pretty much anything was on the table. I often thought if I ran out of tear gas, I'd use a flammable liquid and light a little fire in the burrow entrance. Like I mentioned there is often an entrance near the water and emergency exit higher than the entrance, which is likely to make a decent chimney effect.

The best luck I had was walking the banks and looking for sign. The sign isn't subtle, a lot of vegetation knocked down, bald spots where there shouldn't be any. You can see where they entered and exited the water a lot, they leave drag paths or slides.
I'd find a likely area and set up my folding chair with a good view of the Creek. They are often almost as busy as a Beaver. More busy at night, but often out in the daylight also. Best guess is they have a poor digestive system and eat a lot.
In the spring I set out rafts for the Ducks to feed, a safer place for the Ducklings so the Fox don't pick them off so easy. The Nutria often feed off the rafts, I wish I had a good .22 my ,223 explodes them, a shotgun tears up the raft.
Lovage really draws them. I have some plots of Lovage away from the Creek. I cut it, crush it and spread it on the bank in places with a relatively slow current or still water, it sends up a really strong Celery smell. Fermented Corn stalk silage also works, so does rotting Vegies. I've walked up on a feeding spot and seen 4 or more Nutrias chowing down.
If you sit still they don't see you, if you make a sound they are gone. They also hear/feel your footsteps through the earth, they can be hard to sneak up on. They have good ears.