A number of people, on hearing that I plan to use the original AD&D Deities and Demigods in my OD&D Wasted Lands game have given me guff. "If you're bringing AD&D stuff in, it ain't OD&D anymore!" they cry.
Well, folks, I humbly disagree, at least in this case. Using supplemental material from AD&D--D&DG or even Manual of the Planes doesn't alter the essence of the game. The writeups for the gods in D&DG are quite similar to those in Supplement IV, and in many cases simply better and more detailed.
This is all ignoring the fact that once you use all four supplements, OD&D looks a lot like AD&D.
In any case, my use of D&DG is for reference and informational purposes. See, it comes down to how exactly you look at gods in D&D. Some people think they're there to be killed; that's why they have stats. Some people think that's ludicrous, you can't kill a god. I'm somewhere in the middle, I guess.
Years ago there was an accepted trope that to truly kill a god, you had to defeat them on their home plane (where they were something like 10 x more powerful). I'm not sure if this was official, a universal house philosophy, or just something around where I grew up, but it always made sense to me. In second ed. AD&D the concept of avatars was made official, and it's one we always used anyway. The physical manifestation of any deity you encounter on the Prime Material Plane is not actually that deity, just a sort of essence fragment given form. It is these avatars that have stats and can be destroyed. I've pretty much always subscribed to that notion, even before second ed.
And if a god can create any number of avatars, who's to say there can't be slight variations in power between them? This enables me to use Odin (for example) from Supplement IV AND D&DG with no issues--it's just two different avatars.
The essence of OD&D was that it was so damn open. You can do anything with it, go anywhere. Why, then, would you limit yourself by refusing to look at supplementary reference material for other editions of the game that might come in handy? As long as my rules sets are contained in those digest-sized booklets, it's all OD&D to me.