List of the animals are as follows:
(Animal general locations can be found on the map)
Armadillo: Scattered around Arizona wondering in the deserts.
Bear: Found these in Oregon right by where the symbol on the map depicts. Hostile
Beaver: By bodies of water in Oregon
Boar: Generally found roaming grassy areas in Oregon. Hostile
Buffalo: Immediately right when entering Oregon.
Chicken: Seemingly everywhere. But almost always some at the Williamson's Ranch.
Coyote: Roaming around Aspa Hill. Hostile
Crow: Found in both Arizona and Oregon in the skies on the ground. I had the best luck looking around where the Buffalo spawned (Right from entering Oregon.)
Fox: First animal I found. Best luck is to try around towns. Hostile
Jaguar: You can only find these in Arizona just south of the Abandoned Train. Hostile
Raccoon: Lumberjack Woods and many other places. Try roaming around grassy areas of Oregon.
Sheep: Williamson's Ranch is your best bet. But also found in populated areas.
Skunk: Lumberjack Woods, similar to the Raccoon strategy.
Snake: Scattered around Arizona. Hostile
Vulture: Fort Ghost often has some, but can be found in various other random places.
Warg: Only found in Oregon. Always found mine near the crows and Buffalo. They are black with red eyes. Hard to miss. Hostile
The Beast : There is only one of these in the whole game. It is found in the bottom left hand corner of Arizona. It is a small yellow hoping creature. Looking very much like a Jama-Jama. Picture Below