Nowhere in the book does Ruth Plumly Thompson describe Wag as wearing blue pants, but John R. Neill consistently draws him with them. Incidentally, I originally tried searching for "Wag Oz" and didn't come up with anything relevant, but did get this as a result. So I guess it wasn't a total loss. ;)
When Wag is first introduced, he's the companion of Ruggedo, the former Nome King, who's taken up living in a cavern underneath Ozma's palace. While Wag recognizes Rug's nasty personality and scheming tendencies, he also finds the Nome amusing, and is paid by the former Metal Monarch in jewels and stolen goods. When Ruggedo comes across a box of mixed magic, he tests out an Instantaneous Expanding Extract on Wag, making him grow to an enormous size (about six feet tall on his hind paws, I believe). Thus, he joins the ranks of oversized Ozian animals like the Woggle-Bug and the Frogman, and later Percy the Personality Kid. From the beginning, Wag is kind-hearted and short-tempered, and hitting his head in the process of growth adds the new character trait of being mixed up. He often speaks in spoonerisms, or uses the opposite of the word he means ("come ashort" instead of "come along," for instance). It's kind of a cheap characterization, I'll admit, but it works. I've always liked Wag, and he has a major role in one of the manuscripts I'm working on.
So where does Wag live now? The end of Kabumpo implies that all four main characters settled on Sun Top Mountain after Prince Pompadore's marriage to Princess Peg Amy, but Lost King and Purple Prince have the two of them and Kabumpo residing in Pumperdink. There's no indication of Wag being there, though, so I take this to mean that he remained on Sun Top.