Most of these sorts of immortals are only mentioned in this book, but Gnomes appear quite frequently in Baum's body of work. In the Oz series, he drops the leading G from the word, and gives the Nome Kingdom an antagonistic relationship with Oz. We also catch occasional glimpses of other kinds of immortals, like the enormous Gigans of "Nelebel's Fairyland" (who are turned into tiny Rampsies during the course of the tale), the Governor of the Goblins in The Enchanted Island of Yew, and the Rain King. In their own Oz books, Ruth Plumly Thompson brings in the Sandman (who, if we use Baum's classifications, might count as a Sleep Fay), and John R. Neill works in the leprechauns and kelpies of his ancestral Ireland. Fortunately, the Oz universe is large and varied enough to accommodate these newcomers.
While the official Oz books never mention the great Masters, I've seen a few apocryphal works that utilize the Master Woodsman Ak. Ray Powell's crossover story, The Raggedys of Oz, presents us with all three Masters plus a new one, Aero the Master Airman. Since the role of the Masters largely seems to be to serve the needs of mankind, maybe Powell was thinking that humanity's increasing presence in the air would necessitate this new Master.
One oddity is that, while we see immortal representatives of various sorts of living things (trees, flowers, animals, and humans), and of three of the four classical elements (Nomes for earth, Water Sprites and mermaids for water, and sky fairies for air), fire is largely ignored. There's the fairy Firelight in Tik-Tok, but she appears to only represent the light of fire, not its other properties. Since Baum did give us both the Demon of Electricity and a maiden of electric light, however, perhaps he considered guardians of electricity to be twentieth-century equivalents of the old fire deities. We meet people made of fire in both the Thompson and Snow books, as well as a salamander (the fire lizard kind, not the amphibian sort) in Captain Salt in Oz, but with no indication that they're of the ranks of immortals. I've actually incorporated several jinn into my own Oz writings, with the Red Jinn serving as somewhat of a precedent for this.
I suppose that's about all I have to say on Ozian and Baumian immortals, aside from a mention that Santa himself had to be made immortal with a unique mantle, while Lurline could apparently do the same thing to everyone in Oz with no such assistance. There does appear to be a difference between simply being immortal and being AN immortal. I feel that, essentially, Santa has become a full-fledged member of the pantheon of guardians of the world, while the Ozites merely live forever due to the grace of Lurline. This Ozian immortality could potentially be removed, while I don't think Santa's could (unless perhaps the elusive Supreme Master were to intervene). Nor is Ozian immortality quite as thorough, as there are occasional mentions that Ozites can die (or at least become incapacitated to the point where it makes little difference) due to "total destruction." I wouldn't be surprised if it's impossible to totally destroy someone like Ak, Lurline, or Santa.
Wow, this post ended up being a lot longer than I had anticipated, and most of my friends list probably isn't going to read it anyway. But if you ARE an Oz fan (or even if you're not and decided to read the entry anyway), let me know what you think.