I think the Diablo III story isn't as bad as I thought it was. By that I mean I came up with a charitable way to interpret it.
In Diablo the hero went down into hell, killed Diablo, and put Diablo's soulstone in himself in the hopes of being able to contain the evil. Diablo 2 tells us that plan failed spectacularly and the hero became the Dark Wanderer who went east to free his brothers Baal and Mephisto. The heroes of that game killed Andariel, Duriel, Mephisto, Diablo and Baal. The gameplay only explicitly contains the destruction of the soulstone of Mephisto, but since the heroes acquired the means to destroy soulstones, one presumes they destroyed those of Diablo and Baal off camera.
So in Diablo 3 we discover that this was basically all part of Diablo's plan. Diablo fathered a human child with Adria to be the vessel for his eventual return. The black soulstone was to house the spirits of all the lords of hell so they could be combined into a single body powerful enough to battle heaven. Presumably Adria ensured the loose souls of the five lords of hell already in Sanctuary made their way to that stone. All that was left was to find someone powerful enough to kill the last two lords of hell and imprison them in the black soulstone as well.
In Magda's lore entry, she indicates she took over the coven by poisoning the leaders with the assitance of another witch. Clearly that witch is supposed to be Adria. The coven, though, is in the service of Belial while Adria is secretly in the service of Diablo - supposedly Belial's opponent in the civil war in hell.
So here is the part that is up to interpretation: Is Belial in on the whole thing? One suspects that the seven lords of hell are not all on board with falling completely under Diablo's control by being imprisoned in the body of the Prime Evil or they would have been able to get that done without so much run-around. But Belial acts in a manner that suggests that either he is a complete moron and a terrible liar, or that he is backing Diablo's plan to take on heaven. Maybe he hopes to retain some influence when the lords of hell are one - or maybe he's just so big on taking down heaven he's willing to pay a steep price to do so.
What does Belial do in Act II? He draws you away from Caldeum by sending Magda to Alcarnus. He uses that distraction to capture Leah. Stupid Belial then doesn't kill Leah for absolutely no reason. Devious Belial wants you to think Leah is in danger but really just feeds her information about where to find her mother.
Adria sends you off to get the black soulstone. Belial contacts you as Emperor Hakan to give you advice on finding the black soulstone. Stupid Belial does this because he's futilely trying to convince you that he's not Belial and keeping and eye on you. Devious Belial does this because the whole plan rests on you getting the soulstone.
Once you have the soulstone and thus the apparent means to defeat Belial, he launches an attack on Caldeum. Stupid Belial does this because... I don't know, he's bad? Devious Belial does this because he wants to force you to attack and trap him in the stone.
If it weren't for the generally terrible writing in the game I might have realized all of this much sooner. It makes far more sense to interpret Belial as a master of deception with a long-term plan than as a big stupid lout. Azmodan would be the big stupid lout in this story, tricked into attacking Sanctuary by Belial so that he could be killed and imprisoned.