Import anacondas..a bio-friendly, environmentally-safe means of nutria control...
That or a cajun. They eat these things all the time.
Shoot'em and skin'em. Nutria fur is highly prized. My guess is that is where they came from. Somebody probably bought a couple thinking they were going to become fur ranchers and got tired of the process and turned them loose.
Actually another thought, which goes back to an earlier post. Turn Pit Bulls loose on them. Pit Bulls love to kill things and this way they could be doing something useful rather than killing little kids.