This is not good news for those of you in California.
These critters are awfully destructive, their taste, while edible, is nothing to write home about, and their pelts have never been worth much. But they do have some value, and you can always tan the pelts yourself and sew them into garments, if you're so inclined. I imagine a bunch of them would make a nice warm sleeping bag.
A few states and counties have put a bounty on these critters, to help keep them in check. Most money made from these mini-beavers come from the bounties, not their pelts.
I've never seen stretchers for nutria offered commercially. But you can make them yourself, from wood and a few hand tools. For large nutria, the board should be 4.5" wide at the top, 5.5" at the shoulder, and 5.75" at the base. For small nutria, the dimensions are about 3.75" at the top, and 4.5" at the shoulder and base. All boards should be smoothly tapered, and at least 36" long.
There isn't much literature about lures for nutria. In most cases, they are numerous enough that no lure is needed. However, wintergreen oil does seem to be the best lure for them.
If I were trapping nutria, I would use a variation of one of my raccoon-muskrat lures. I would use 1/3 spearmint or peppermint oil to 2/3 wintergreen oil, shake it a little, and let it age at least a day. If I catch a nutria, fine; if I catch a raccoon, better. Drowning rigs should always be used.