Udyr is not a Vastaya
Udyr is a martial artist.
In martial arts, it is common to have different battle stances or styles named after animals.
Take for example in Kung Fu Panda. There's "Snake, Mantis, Tiger, Monkey, etc."
Udyr is not a Vastaya who transforms into different animals. You don't see him do that unless he is in his Ultimate skin. Even then, it's more of a spiritual connection where he summons the animals spirit as some sort of oversoul. In which case, it's more like his inner Chi or Chakra appearing akin to Naruto's Kyuubi.
Udyr has 4 fighting styles: Bear, Turtle, Tiger, and Phoenix. He does not physically turn into them or channel said animal (unless we're speaking Godyr). He merely adopts the martial art combat style for them.
