Gluttony: Even newborn babies need alcohol to get through the working day. Eating in a legendary dining room will offset any tragedy these short hairy hedonists face.
Lust: Wink wink, nudge nudge, say no more.
Greed: The dwarves so value shiny trinkets that failing to present sufficient tribute to your rulers is punishable by death.
Sloth: It doesn't matter that the fortress is on fire, invaded by skeletons and out of food, if a dwarf wants to have a break, or a nap, he
will.
Wrath: Obvious. The dwarves' natural response to unhappiness is to hurl objects about or attack someone or something.
Envy: The dwarves are quite open aboout demanding better lodgings, dining rooms and burial arrangements than those they consider to be below their station.
Pride: The engravers often engrave murals commemorating legendary engravings they made themselves. The best thing that can happen to a dwarf is making an artifact. One of the most common activities in a dwarven fortress is building giant projects to make your name go down in history.
Also: The elves obviously represent Jesus. They want your dwarves to abandon their evil ways and join them in living in harmony with the universe and being kind to animals. And then you kill the diplomat they sent to forge better relations between your civilizations.
The goblins are such an obvious allegory for the Antichrist that I won't even bother explaining it.