Nutria are Class: Mammalia, Order: Rodentia, Family: Myocastoridae, Genus: Myocastor, Species: coypus.
Weasels are Class: Mammalia, Order: Carnivora, Family: Mustelidae, Genus: Mustela, Species: (various).
Rats are Class: Mammalia, Order Rodentia, Family: Muridae, Genus: (various), Species: (various).
Nuria are not of the 'weasel family', nor any kind of rat...not even close to either taxonomically.
As for foods eaten, I have eaten all on your list and can add to it: Cane rat, bat, domestic dog, various worms, various grubs, various beetle larvae, various spiders, various snakes, various lizards, turtles, mice, jellyfish, sea cucumber, koumis, blood, and a number of other things that I cannot remember offhand.
Interestingly, I will not eat cilantro, blue cheeses, Wonder bread, or Twinkies.