Elfen Lied Abridged Series are parodies chiefly inspired by the Elfen Lied anime series. There are many sets of these, the most famous web-wise being one created by Bennett The Sage, now known (as of late 2012) as Draculas and Licorice, seen chiefly on YouTube, from where it was removed because of a dispute resulting from a joke in an episode flagged as violating YouTube's terms. (No new link has been found as of this article's creation.)
These parodies operate by dubbing snarky, sarcastic dialogue over the original in the series. Examples would be pointing out seeming plotholes or things glossed over, or events that the anime begins but we never see resolved, except in the manga, which may in fact be commented on. These parodies may be sounding boards for (or light mockery of) fan disapproval of certain story elements, like Kouta and Yuka being cousins.