First of all, I'd like to clarify that Elfen Lied is not the horror-violent-awful anime that you think. The story of the series is incredibly awesome, its really beautiful and touching, the bloody massacre scenes are just to complete the story. If you are afraid of watching it beacause the blood, deaths etc.. go on dear. You'll love it. I'ts the best drama anime I have ever seen in my life. And i'm happy I faced it.
Story: As I said, there's no anime story like that. Basically it's around the diclonius lucy and her traumatic past consequences. But the supporting characters arent left behind. Each of them have their function.
Art: The drawing style is really pretty and clean, though I dont like some details. The bloody scenes are really good illustrated and also the effects.
Character: I love all the characters basically >.< Each one of them have its own dramatic past, wich left a lot of trauma and sadness on their lifes. Each one is really well developed.
Enjoyment: Men, i'ts perfect! 100000000000 LOVE IT! I'm sure you wont be dissapointed!
Overall: Resuming.. this anime really deserves all its fame, cause its a life lesson to all of us; humans.
*sorry 4 bad english, i'm brazillian..*