I would like to write an RPG licensed under the OGL that draws inspiration (but does not contain any copyrighted material etc.) from novels and other forms of media. How could I reference those books in my game to credit this inspiration? Additionally, how could I cite other RPGs/RPG supplements as inspiration?
You should absolutely not put it in the OGL statement. The OGL statement is a very specific licensing contract only to be used on other OGL works.
If you just "draw inspiration", you can put that in your game's actual text wherever/however you want. This has absolutely nothing to do with the OGL, whether your game is OGL or open licensed or closed or what. Some game writers put a big list in an appendix to follow the "Appendix N" tradition of AD&D. Others just say it organically often in their introductions, like Blowback says something like "this was inspired by shows like Burn Notice" if I recall correctly.
But you better be sure you're just drawing inspiration and not copying anything. Copying anything is a whole different thing and is never legal without specific agreements. So a product like Redhurst can be a kids magic school, but if it gets anything (names, characters, etc.) put in it directly from Harry Potter it's lawsuit time.
Technically this works the same with RPGs, but once you get to "RPG supplements" you are starting to really tread close to the line between inspiration and stealing. Frankly even listing them contributes to the idea you may be stealing; I'd step back and not credit other RPGs and if I felt strongly about doing it, I'd look a lot closer at what I'm 'borrowing' and determine whether that's appropriate or not.
I'm concerned by your question about putting novel inspirations in the OGL that you do not have a basic working understanding of copyright, the OGL, licensing, etc. You should take it upon yourself to go get a correct working understanding before publishing any RPG.