Neither Curse of Weakness, Demoralizing Shout, Demoralizing Roar nor Vindication stack. The curse is superior with no talents involved, but comes at the expense of the warlock not being able to cast Agony or Elements, decreasing damage output. When fully talented, both Roar and Shout reduce AP by 575 at level 80, while the curse and Vindication 'only' reduce it by 574.
Improved Curse of Weakness increases the amount of attack power reduced by the curse by 20% at max rank.
Curse of Weakness is an Affliction spell, and thus gains the benefits of Suppression, Improved Drain Soul, Grim Reach, and Contagion talents.
Tips and tactics
On players, DPS is decreased by 1 for every 14 attack power; an attack power reduction of 350 thus corresponds to 350/14 = 25 dps.
On mobs and bosses, there are other factors between AP and damage, usually giving much more damage for the same amount of AP. This can make Curse of Weakness a very good option in certain situations.