Diablo 3e took a turn that would be best avoided: completely emulating the powers and progress of the game. Take a peek at Warcraft d20, from S&SS for a much better adaptation. They wanted to make D&D in the world of Warcraft, not turn D&D into a pen-and-paper version of the crpg mechanics.
If you want to give the Diablo players a taste of Diablo D&D, just use a very basic plot from Diablo 1: The village the PCs grew up in is being haunted by otherwordly creatures that supposedly lair deep below the ruined cathedral in the outskirts of the city. The village elders send a message to the PCs, who must venture down the crypts and catacombs of the cathedral to find out just what turned the cathedral into a focal point of evil. Ask the players what are their favorite Diablo (1 or 2) characters, and explain that arcane spellcasters will have a hard time if they try to wear armor.
Here are some quick rundowns of the classes and what they can mean in D&D terms:
Amazon: Bow or Spear specialists. A Fighter with archery feats or a spear-wielder with Power Attack will do nicely.
Assassin: Martial Artists that keep arcane spellcasters in check. Monk will do fine, although Diablo 2's Assassin have some shadow/psychic powers. Monk/Shadowdancers would be great.
Barbarian: can Rage and Dual-wield. Barbarians cover most of its abilities.
Druid: Shapechage and summon nature's ally, so go straight Druid.
Paladin: Has auras that increase effectiveness. Most Diablo2-paladin abilities are covered by feats in Defenders of Faith. Go with Paladin or Cleric.
Necromancer: Actually a priest that venerates death. Not a good PC, due to the tendency of raising skeletons. A Cleric of Wee Jaz is the closest analogy.
Sorceress: Works just like a Sorcerer that learns mostly fire, lightning and cold spells.
Rogue: Diablo 1 had this class, which can disarm traps and is very good with a bow (but less so than an Amazon). Go with Rogue, plus some archery feats.
Hope this helps!