If I had to nominate a single product for the category of "weirdest RPG I've ever owned," there's a good chance it'd be the 1982 book Fantasy Wargaming, edited by Bruce Galloway and written by a number of (presumably British) authors I've never heard of. I bought my copy back when chain book stores still sold gaming products in large quantities, by which I mean that they not only stocked many copies of most products but also sold products by companies other than TSR. I can only presume that gaming was still enough of a fad in 1982 that someone thought it'd be a good idea to offer this bizarre book for sale. Of course, I bought a copy, so I guess they were correct!
I call Fantasy Wargaming "bizarre" for a number of reasons. Firstly, there's its title. Now, I'm probably the last person who'd ever complain about a RPG that proudly proclaims its connection to the earlier hobby that spawned it. Yet, by 1982 (or even 1981, when the introduction was written), almost no one -- certainly no one inside the hobby -- used the term "fantasy wargaming" to describe Dungeons & Dragons or other RPGs. It's true that, as late as 1976, TSR still subtitled D&D products "Rules for Fantastic Medieval Wargames Campaigns," but that usage had been discarded years before this book was published. Consequently, Fantasy Wargaming had an odd "out of time" quality to it when I first bought it, as if it'd been trapped in amber since the days when dinosaurs ruled the earth and the term "roleplaying game" had not yet entered common use. (To be fair, they do use "roleplaying game" in the text occasionally and note that it is roleplaying that distinguishes fantasy wargaming from other types of wargaming.)
Another reason I deem this volume bizarre is the disdain it exhibits not just toward existing RPGs -- that's a fine old school tradition -- but toward roleplaying generally. The authors I surmise based on comments here and there were Napoleonic wargamers at Cambridge who one day decided to give "fantasy wargaming" a whirl to see what all the fuss was about. Though they enjoyed roleplaying as "pure escapism," they nevertheless found it lacking and this book is the result of their attempt to correct the deficiencies they saw in it.
Most of those deficiencies were in the realm of "realism," something that powerfully dates this book as a product of the late Golden Age, when dueling articles on the physics of falling damage were regular contents of Dragon. Of course, the authors of Fantasy Wargaming were much more interested in social/historical realism, which is why the book is filled with broadsides against most fantasy, both literary and gaming, which fails to take into account this or that little bit of trivia about the European Middle Ages. The end result of this is a game -- assuming it is even playable, which is far from certain -- whose nitpickiness about historical minutiae puts Chivalry & Sorcery to shame.
Unlike C&S, though, there's not a lot in Fantasy Wargaming that can be profitably mined for other games. There are some interesting bits about historical arms and armor and social structures, but all of that could be found in better written and detailed scholarly books. Beyond that, perhaps the most entertaining section is the ranking and stats for the hierarchy of Hell, with a corresponding ranking of the powers of Heaven -- just in case you ever wanted to know the combat abilities of the Blessed Virgin Mary or St. Francis of Assisi. Most rules are written both suggestively and opaquely. That is, they imply much but say very little. That's probably why, as a youth, I remained convinced that Fantasy Wargaming was a playable game, even though I never actually inflicted it on my friends, as I did DragonQuest.
So why did I ever buy this book? It's hard to remember this, but, even in 1982, roleplaying was big. It was a huge, huge fad and, while the total volume of product was probably much smaller than what is released today, there was still enough of it, available through a wider variety of outlets than nowadays, that I was offered many opportunities to dabble and see what the hobby was like outside the TSR/D&D orbit. Sometimes, this brough into contact with gems like Call of Cthulhu, but, more often than not, it gave me stuff like Fantasy Wargaming. At the time, I was looking to shake up my D&D campaigns and inject a bit more "realism" into them. I quickly realized that, even if that goal were itself a worthy one, Fantasy Wargaming wasn't going to help me achieve it.
The funny thing is that I still own a copy of this book. For all its oddities -- or perhaps because of them -- I pull it off my shelf every now and again and read through it, if only to remind myself that, while its focus may have shifted over the years, the craziness of gamers has remained a glorious constant of the hobby for as long as I've been involved in it. May that never change.