The reason Urotsukidoji is fairly nonsensical is because it was originally made as a series of 50-minute
OAV's. The first film was the first three episodes, the second was the next two. So the first film started out at roughly 150-minutes, was cut down to about two hours, and then further
censored. That much removed from the story leaves the plot a little muddled to say the least. It's a shame because the story to the first film is really quite good, despite the poor
dubbing and
translation (another factor to the confusion in the story). Perhaps the
manga on which it's based is good, but I don't know, I've never read it. There is however, like most japanese films, a lot of symbolism revolving around adolescence, and psychology (i.e the ego, the id and the superego being reflected by the three worlds or human, demon, and jyujinkai), but it's only there if you know it's there and also lost in translation.
The story is about a brother and sister (the sisters knickers are permanently showing, when she's actually wearing them that is), from the world of the jyujinkai (man-beasts) who are seeking the Chojin (overfiend) who will unite the three world of human, demon, and man-beast. They both have their own ideas about who it might be, although we have no idea how they came to this conclusion. There's lots of complications in the way of jealous lovers and things like that, and in the end the world is destroyed by demon cum. Lovely. And yes, the plot does get carried on from there in part 3.
The second film is also quite confusing in that it's set somewhere in the middle of the first film, and the continuity isn't right. It's also an utterly pointless story and a terrible film. Unlike the first film, none of the sex scenes are excused by the plot either.
Having said that the second film is utterly pointless, it does serve to introduce the character Munehausen, who features in part three. But then parts three and four are atrocious and also suffer from being cut so the plot makes no sense, particulary part four which had two of its three parts banned outright in the UK and the feature length finale cut to less than half it's length.
Urotsukidoji is probably something an anime fanboy (or girl) should see just for reference, but it's not really worth watching for any other reason besides curiosity. The plot to the first film doesn't fully resolve and everything from there on is terrible.