Dodge, parry and block are all independent events (http://www.tankspot.com/forums/f63/3...bat-table.html)
If you dodge an attack, you take zero damage. If you parry an attack, you also take zero damge and your next autoattack swing is sped up a little bit. If you block an attack, a fixed amount of damage is removed from the hit you take (http://www.tankspot.com/forums/f63/41527-blocking.html). Dodge and parry are called avoidance, and block is a form of mitigation.
Using that, if you have 18% dodge, 18% parry, and 18% block, you have a combined 36% chance to take no damage, and then 18% chance to block some of the damage of a hit. Dodge, parry, and block do not work on most magical effects (though they work on the melee attacks of elementals which deal fire/frost/whatever damage)
Parry does not depend on weapon at all except in that if you parry an attack, you get that little bit of speedup on your next autoattack.