Slightly inaccurate. Central Oregon doesn't support a nutria population, too cold. Would have been western Oregon.

Just an aside, since so many Californians have moved north (an invasive thing in itself) maybe it's only fair we send some invasives down south.

My understanding is that they were first introduced to Louisiana in the early 1930s for fur farming, (and as a meat source later). In the early 1940s, a hurricane hit the state, and among the damage caused the destruction of several nutria operations, resulting in nutria escaping. There were also many nutria releases owing to the collapse of fur markets.
Also, in the '30s fur boom, they were introduced in Oregon, Washington, Michigan, and Maryland.
As far as I know, there are no nutria in Maryland or Michigan anymore. of course they are abundant in Louisiana, and as beaverpeeler said, the western part of Oregon has a very large population. Not sure about Washington, but sure could be nutria in the southwestern coastal and Columbia River Basin areas of that state.
I find it interesting that the San Juaquin Valley in California would have a population that is expanding. That area is industrial agriculture and would think that any nutria problems would be addressed and neutralized rather quickly.

Fun fact about nutria for those who don't know, the females have their teats on their backs, so the young can nurse while swimming.

yep. Learned that on the first one I tried fleshing. I wasn't very good a fleshing back then, (not an expert now, either!), and managed a couple holes right off. Once I figured out paying attention to that area it went a little better.