Book sources for this project are divided into two camps: literary sources, and derivative works (which for the most part are games). In addition, there are some games which have nothing to do with the original premise but may still be useful.
This list is meant to be evergreen and may be expanded in the future.
Moorcock, M., Elric of Melnibone (omnibus) (London, Millenium/Orion, 1993)
Moorcock, M., Stormbringer (omnibus) (London, Millenium/Orion, 1993)
Moorcock, M., Earl Aubec (short stories) (London, Millenium/Orion, 1993)
Moorcock, M., Corum (omnibus) (London, Millenium/Orion, 1992)
Moorcock, M., Von Bek (omnibus) (London, Millenium/Orion, 1992)
Lovecraft, H.P., Complete works of H.P. Lovecraft (Cthulhuchick epub)
St. Andre, Perrin, Monroe, Stormbringer 4th Edition (Chaosium 1990)
Willis, Watts, Elric! (Chaosium 1993)
Petersen and others, Call of Cthulhu 4th Edition (Chaosium 1989)
Of Moorcock’s prolific offerings, the most pertinent are the various Elric books. Unfortunately I’m not familiar with the most recent anthologies, which are published by Gollancz, and may have different orders of contents from the older Millennium imprints that I own (the original, big format books, lovely though not very portable). Wikipedia has a good run down of the books in roughly chronological order, and the Wikiverse project is also a source of information.
In addition to Elric, the other books recommended are the first Corum trilogy (Prince in the Scarlet Robe), the short story Earl Aubec) (from the anthology of the same name), and The Warhound and the World’s Pain (Von Bek). I chose these because they’re fairly suggestive of the relationship between humans and gods (and Law and Chaos).
For reference, I originally used the 4th editions of both Call of Cthulhu (hereafter CoC) and Stormbringer (hereafter SB). I also posess most of the Elric! line of books (technically these are Stormbringer 5th ed) and the first edition of books published by Mongoose in their Eternal Champion line (EC).
That’s all well and good, except none of these books are in print now. Mongoose’s offerings are defunct, which means there’s no official game based on Moorcock’s work currently available. This leaves the secondhand market as an option for obtaining copies of the various games.
However, I’m lead to believe that Chaosium’s recently released Advanced Sorcery (for Magic World) contains the content of the Bronze Grimoire from Elric!, and should include rules for demons and elementals. I can’t confirm this myself and I don’t intend to buy the new book any time soon, so caveat emptor.
Call of Cthulhu is of course available, in the 6th (and soon to be 7th) edition. One supplement I got a lot of mileage from is the Cthulhu Dreamlands hardback; since Moorcock also has a take on the Dream Realms (q.v. The Fortress of the Pearl) and there has even been a Mongoose game supplement of the same name, it may be worth consideration.
A final note regarding the various Eternal Champion games. I haven’t mentioned Mongoose’s Elric of Melnibone line, mainly because I don’t really like them as games; part of me never really warmed to the Mongoose way of doing Runequest. I’ve also complained about the presentation of the books in the past, and I confess this has put me off reading them cover-to-cover. However I have enjoyed the parts I’ve read and for the Moorcock faithful they may prove to be a better and more complete representation of the Young Kingdoms (and the Tragic Millennium, for Hawkmoon fans). If the presentation of the Elric game was fixed in Mongoose’s 2nd edition, that may be the version to try to pick up second hand (they did a good job for MRQ2).
If you’re not wedded to the original games, there are plenty of other options that could be used to emulate the hybrid world. Games will most likely still be oriented towards investigation, which makes Trail of Cthulhu and other Gumshoe games worth considering (and if you’re quick, you can pick up the Trail in the latest Bundle of Holding). I can recommend the Rough Magicks supplement, at least for Kenneth Hite’s essay on Lovecraftian Magick.
Other titles to consider are Unknown Armies, the free Nemesis) (which includes sanity rules from UA) and Kult. However these all deviate into modern urban fantasy/horror, so will require some amount of surgery to make them fit together.
If you want to play something more epic and/or narrative oriented, consider simplifying. Everway is out of print and feels a bit too optimistic to me, but it could work. If you like to get your hands dirty, hack Apocalypse World. This really is deviating from my original specification, but whatever, if you’re inspired then make the game your own.
On the subject of “epic”, the Eternal Champion’s high fantasy (with anti-hero) presentation does clash with Cthulhu’s everyman nihilism. This is something I’ll cover later, but for now it’s worth mentioning that if you just glue Stormbringer and Call of Cthulhu rpgs together, you’ll probably get a campaign where some characters can go toe-to-toe with Lovecraftian baddies, at least until they go insane. This may not even be a bad thing: if the goal is to interrogate the higher powers on their motivations and their place in the cosmic scheme of things, then having characters (and therefore players) with the ability to ask such questions may be a benefit.