Well here is my little theory on what is going on. Souji has a split personality which is Kazu. Whether or not who is the real personality I do not know. However I believe The "stronger" personality is Kazu and Souji (the main character) was created in order to cope with something that happened in the past. Which was most likely Kazu/Souji killing someone.

Now about the three murders that happened were most likely committed by Souji/Kazu. He killed them because I believe in chapter 3? Kazu mentioned killing people he only acknowledged. The people who died were, a president of the school, a track ace, and a genius. All of whom are possible competitors to Souji/kazu. In chapter 3 there appears to be a 4th body whom is not identified. This body is most likely the first murder that Kazu/Souji committed. The 3 sisters are just there to comfort Souji and keep him contained. I believe they are doing so because they love him more then one should.

Now, let us go more in depth is Kazu and Souji. It is obvious to say that I think Kazu is the original personality because Kazu is referred to as onii-chan by Souji and his sisters. So Souji being created is the "younger" one. Other elements in the story such as the genji story that was told and teacher expressing his thoughts about DIDS. This is probably just made to make us think there is a multiple personality disorder, or he is just screwing with us.

The recent dreams in chapter 7, and 8 are visions from the past. However I have no idea how they correlate to the story in anyway. However from what I can gather these are the ancestors of the family. And it seems they had an ulterior motive for their descendants. Though I have really no idea and that is just a long shot.

I predict in the end Souji will come to realize he committed all the murders and attempt to confront himself. He will fall into a hole of despair after realizing that he committed them, and that he is the false personality and the story will probably end in tragedy.