There was a time when I hunted them fairly often. We knocked back the numbers to manageable levels and now they have a season here.
Depends on the habitat how you hunt them. And what the regional law allows. Where I hunted them was a steep banked Creek. I used a dog to find their burrows. marked them with a flag. Or you can see where they have been feeding, I've watched them harvest grass on the bank, they cut it with their teeth like a scythe and leave what looks like a freshly mowed lawn behind. Best luck is IMO Jack lighting (flashlight on a shotgun) them. They are mostly nocturnal.
I'd check on local laws, but you can spot a burrow that looks used and fire tear gas rounds in there (I have an old tear gas revolver). Have somebody standing by with a shotgun, they come out of the burrow like a rocket.
Nutria can really do a number on the landscape, between the burrows on the creek bank and eating all the vegetation that keeps the bank stable, they can change the course of Creeks. We got a permit to clean them out and to hunt them any way we could for a few years, they were really screwing the Creek up.