General Background
I have not found any books that were written only about Eastmoor. However, there are some general histories of Columbus that may talk about Eastmoor and adjacent communities. This can help provide you with an overview of the area.
This subject heading: Columbus (Ohio) -- History is a good start to see what is available. However, while Otterbein has a few books on Columbus history, I would recommend going to the Columbus Metropolitan Library for more depth.