All three of those dishes are originally Creole, but Cajuns have their versions as well.
I've seen enough red beans and rice in soul food restaurants that I'm okay with it being called soul food. It's migrated into the rest of the deep south. I grew up with it. (By the way, the "hot dogs" in that pic are sausages, most likely andouille.)
I wouldn't count the other two, though. They're southern, but they aren't soul food. If you find them outside Louisiana, it's most likely at a Cajun or Creole restaurant. You might find red beans and rice at a fried chicken place in South Alabama. You won't find jambalaya or gumbo.
For Grimson's original question, the traditional New Year's meal is one of my favorites—black-eyed peas, greens, cornbread. I usually make a Hoppin' John with the black-eyed peas. The prep is close to red beans and rice, but (obviously) the red beans are replaced with black-eyed peas.
I gave up fried foods awhile back, so that knocked out a good chuck of the meats—fried pork chops, fried chicken, fried catfish, country fried steak, etc. But I still make things like smothered pork chops and catfish stew. And I still love fried okra. Sometimes, you have to make exceptions. Shrimp and grits is another favorite. Cornbread dressing is a requirement at Thanksgiving. Cane syrup is pretty much perfect. I could go on for a long time with this list.
