Akali is really powerful ninja,u can easily slain your enemies,by Shadow Dance and in the same time u can use it for escaping ;)
Akali's Twilight Shroud is really useful when you are fighting against more powerful enemies, this spell can slow them and u can help ur team by that or using it to attack ur enemy from behind and killing him no matter how well he plays.

Mejai's soulsteal is powerful item early in the game, when u reach 20 stacks u will have +160 ap and cooldown reduce, ofcourse u need magic penetration and movement speed and Lich Bane is one of the most needed items for Akali. The head will increase ur ap drasticly, spell vamp, slows are useful stufs in a battle. ;)