Zombies, Creepers, and other meaty creatures (but not spiders) have a reduced resistance to Slashing Damage.
Piercing Damage is completely useless against skeletons; other mobs resist about half.
Crushing damage is done by Maces.
Skeletons have a reduced resistance to Crushing Damage.
General damage refers to both falling blocks and vanilla damage types (fall damage, fire damage, suffocation, and Enderman attacks). General damage causes full damage to a player with or without Armor, and damages Armor for the full amount the player takes.
Explosion damage counts as General Type, and is done by Creepers and Powder Kegs. Explosion damage scales with proximity, meaning the closer the player is to the source, the more damage that will be dealt to the player and armor.