Story: Usually when I write reviews for OVAs I use this time to just rant about how the story is pointless and is nothing but 20 minutes of fan-service, but this particular OVA was just as good as the actual series of Elfen Lied, if not better.
Set in the middle of the Elfen Lied TV series, this OVA depicts Nana's daily life in Kouta's house as she learns to deal with living in a typical(ish) Japanese household. The part of it talking about Nana was funnny, and a nice release after all the hightened seriousness of the TV series of this anime, it actually WAS humourous too.
Then there was the second part of this OVA, which provided background information on Lucy's story- it tells of a young human girl who befriends Lucy, only to be killed. This part was significantly important and filled in a lot of the gaps from the original anime, as well as making you sympathize with Lucy a lot more. It was immensely interesting to find out why Lucy has such an intense hatred for Kuruma, and the whole thing was explained beautifully.
Suprisingly I wouldn't say there was actually not that much fan-service in this as I expected, yes there was some, but no more than the standard Elfen Lied episode contains. It didn't override the whole show, and it seemed pretty subtle as far as OVA's tend to go in the ecchi category.
Animation: Nothing different from the TV series, this animation is very good ^^
Sound: Also like the original show, the music in the Elfen Lied OVA is very good and suits all the different moods of the anime.
Characters: For an OVA characters are excellent, seeing both Nana and Lucy develop is interesting and nothing like any other OVA I've seen before. Not much is really seen of the other characters, but out of all the others theres only really Yuka and Kouta left and I don't like them anyway- so that didn't really other me that you never saw them :)
Overall: Don't underestimate this OVA- It could have been an extra episode of the anime secreted in the middle, it was so good. I'd definitely suggest watching it if you like Elfen Lied, or just want more background of the characters.