Prime Evils
Diablo- Lord of Terror
Mephisto- Lord of Hatred
Baal- Lord of Destruction
Lesser Evils
Azmodon- Lord of Sin
Belial- Lord of Lies
Anadriel- Maiden of Anguish
Duriel- Lord of Pain
Other Characters:
Tyreal (Angelic Guardian)
Izual (Lt. of Tyreal)
Cain (Horadrim Mage)
I'm pretty newb, but I know the story pretty accurately. If you read the book in Diablo 1, you'd know that the forces of Heaven and Hell were and still are fighting each other. Diablo, Baal, and Meph are the strongest and eldest of the 7 evils, and that already built some jealously within the lesser evils. When humans first existed, the prime evils were intrigued by their pressence, and thought humans could be used to turn the tides in war. The lesser evils were angered by that, since they thought the minions in hell were far superior than humans would be. A plan was created by Azmodon and Belial to overthrow the Prime evils, and all of Hell went to war with the Prime evils. Eventaully, Diablo, Baal, and Meph were defeated and banished to the mortal realm. To their credit, they destroyed one third of the legions of Hell, or so it says in the story. Once they were in the mortal realm, chaos ran rampant all over the world. A mystic clan of Magi (the Horadrim) were than created to stop the Prime evils, brought together and created by the Angel Tyreal. Using a soul stone, they were able to capture Mephisto first. The second to be captured was Baal, but during the conflict, the soul stone was shattered. To imprison Baal, a Horadrim mage sacrificed himself (Tal Rasha) by infusing a shard of the soul stone within himself to seal Baal within his body. The last to be captured was Diablo, and for a time, peace was brought back upon the lands, until the time came when the evils were back again.
In Diablo 1 storyline, you're suppose to investigate the strange matters that are found happening near the Monestary. Obviously, Diablo's presence has awakened, and has taken control over King Leoric's son. You are suppose to stop Diablo before he regains his lost strength, and sets on a journey to free his captive brothers. In the ending of the game, you manage to defeat Diablo by infusing the broken soul stone shard within yourself, just as Tal Rasha did. However, it was a ruse set about by Diablo himself, for he seeked a stronger vessel to contain than Leorics son. After Diablo was supposedly defeated, the town rejoiced for days to come. However, the warrior who defeated Diablo acted strangely, became reclusive, and then, left town. Shortly after he left, the town was destroyed. That sets in motion the story of Diablo 2, where Diablo has taken over the vessel that captured him, and plans to set free his captive brothers. Anadriel and Duriel, who opposed the Prime Evils before, are obviously back in unison with their elder sibblings.
Other:
Izual, the Lt. of Tyreal, was supposedly one of the holiest warriors to ever exist. His exploits against the prime evils and his minions were well documented. Izual wields a powerful Phaseblade called Azurewrath, which you can find in Diablo 2. (If you're lucky) In the story, Izual was supposed to stop the creation of a powerful sword called Shadowfang. The mission was too much, and he fell to the forces of Darkness. In Diablo 2, when you speak the the spirit of Izual, you find out he was never a pure warrior to begin with. He betrayed Tyreal, and even gave intimate knowledge of the workings of the Soul stone to the prime evils. That was how the Prime evils were able to manipulate the soul stones, and set themselves free.
Anyways, that's all I know. That's probably other things i left out, but watever.