there are books around diablo's lore, though I didn't read any. I'm also pretty sure to have seen some kind of timeline in this site when the game was still under development (it can be still here buried in the archives).
the very very short story:
D1: Diablo was imprisioned in his soulstone, that was hidden somewhere in Tristam's Cathedral. somehow his mere presence was enough to corrupt people that lived nearby, like the archbishop Lazarus. diablo tried to possess Leoric, but Leoric was still a noble person and resisted the possession, maddening in the process. instead of Leoric, diablo made Lazarus bring Leoric's youngest son to the cathedral, and possessed the boy. by then people had already noticed that demons and undead were multiplying nearby. when the kid "went missing", Lazarus pretended to still be a good bishop and led a "rescue party" inside the cathedral; almost no one returned. Leoric, now definitely mad, started decapitations and insane wars; his decisions as king were so absurd that Lachdanan, one of his lieutenants, killed Leoric. and that's where the game starts, the hero just arrives to the terrorized Tristam, the king and his son dead, the archbishop corrupted and disappeared, and the cathedral infested with demons and undead. as we play we descend the cathedral's 16 floors into hell and defeat diablo. but then diablo corrupts the hero too and possesses him...
D2: the former hero of tristam razes the town and leaves, becoming the dark wanderer. he travels east, to free baal from tal rasha's tomb and mephisto from the temple city of travincal. we chase him all the game, finding andariel and duriel in the way, meaning that hell is once again led by the 3 prime evils. diablo succeds, and right after meeting mephisto goes back to hell, as to claim his throne back. we fight mephisto just after that, and chase diablo to hell (meanwhile baal goes to mount arreat). in hell we fin izual, that says (after being defeated) that he was the one who told the prime evils how to corrupt the soulstones, and that it was their plan all along to be imprisioned within them (so there's a masterplan in motion that would possibly end with hell winning the eternal conflict). we defeat diablo, break his and mephisto's soulstone, then tyrael opens a portal back to sanctuary to chase baal (in D2 expansion).
D2-LoD: we kill baal's army as we climb mount arreat, and find that he already corrupted the worldstone. after we defeat him, tyrael says he has to destroy the worldstone or hell would flood into sanctuary. end!