What do Dexterity, Strength, Intelligence and Vitality do? Do they have different effect in each class?
Strength increases Armor by the amount of Strength you have, and increases Barbarian damage the amount of Strength you have as a % amount. Meaning if you have 100 STR you'll have 100 armor and 100% extra damage as a Barbarian.
Dexterity increases Dodge chance, and increases Monk and Demon Hunter Damage just like Barbarian's STR
Intellect increases Magic Resistance based on total INT. For Example, 1111 INT would give you 111.1 Magic Resistance. Intellect also increases Wizard and Witch Doctor damage just like Barbarian's STR.
Vitality increases health.
You can mouse over the stats on your character screen and the game will tell you exactly what they do for your class.