They wouldn't be based on other Pokemon; why would they be? New generations try to vary their designs from previous generations, and each region has its own legends, so there's not really much basis on a Pokemon being based on previous Pokemon.
e.g. Zorua and Fennekin are both fox like Pokemon, but they're based on foxes, not each other.
I don't see your logic on Tornadus-T being based on Lugia/ Ho-oh; by aesthetics they look nothing alike.
In any case:
therian: a mammal of the major group Theria, which comprises the marsupials and placentals.
Theria: a major group of mammals that comprises the marsupials and placentals.
Their original forme is called the Incarnate forme:
Incarnate: (esp. of a deity or spirit) embodied in flesh; in human form
So Therian formes are more animal like and Incarnate formes are more human like. Tornadus looks like a bird, Thundurus looks like a snake/ dragon, and Landorus looks like some feline creature.
Bulbapedia on form differences
(those dictionary definitions came from the dictionary on my Mac)