In my opinion, this book is a mess.
I can only imagine it was written with the expressed purpose of being part of a college courses selected readings. It is written in the style of a scientific paper with constant citations, but the information from said citations is rarely more than a vague sentence that does not impart the valuable information necessary to complete his arguments.
While the style may attempt to be scientific, the tone is clearly conversational. His turns of phrase and poorly thought out examples are clearly written as if he is speaking them to an individual or group, which conflicts with his intention of having a well referenced work of research. On top of this he take incredible care to be circuitous in his phrasing and word choice. Ideas that could be expressed simply and directly, seem not to have imparted his self-believed genius, so instead he takes the long winded and overly indulgent path to express his points.
Writing intention, style and tone aside, he spends at least half of the book discussing monotheism and atheism. The book should contain some information on the two for background and comparison purposes, but why call this "An Inquiry Into Polytheism" if just as much of the writing is an inquiry into monotheism or atheism. Most of his arguments are circular and self-defeating, he will discuss the flaws in monotheist and atheist arguments against polytheism only to turn around and use the same style arguments to attempt to prove polytheism is a more logical idea. The book spends far too much time tearing down monotheism and atheism, and then using that as a basis to bolster the argument for polytheism. The argument that monotheism doesn't address this and atheist are following a wilful ignorance, therefore polytheism makes more sense, is itself nonsensical. Certainly it would seem that many of the points Greer makes in this inquiry are well researched and backed by quality information, but do to his choices to be vague when invoking previous works, the only way I can know for certain is to find and read everything cited in his 8 page bibliography (this is almost as long as most of his chapters)
To wrap this up, I would never recommend this book to anyone, unless they were curious to see how easy it is to get a book published when you can hide it in the guise of intellectual writing and actually have it make no sense and not contribute in any way to intellectual knowledge. Speak in circles, use big words and choose a topic that cannot be proven right or wrong, and you'll be on your way to your first published book.