In Sora's story, Sora is looking for Riku and the King and they arrive at Castle Oblivion. Castle Oblivion is the real weird lookin castle. Anyways, Sora and the gang go into it. Donald and Goofy become cards (still don't know why) and Sora starts through the castle.
As he goes through, he begins to loose more and more of his memories because of a girl named Namine. She is being forced by the Organization (also known as the XIII Order) to mess with Sora's memories. All the worlds we see in this game are the worlds that we were in in the first Kingdom Hearts.
Anyways, Namine replaces herself as Kairi in Sora's memories, so Sora forgets Kairi. Sora fights some members of the Organization and defeats Larxene and fights with Axel. Axel is confusing because he is a double, er, triple agent. He kills Vexen, another member of the Organization who created a Fake Riku who doesn't know he is fake because Namine gives him Riku's memories. Axel lets Namine go.
Namine runs to Sora and tells him about his false memories, and that the only way to set them straight is for him to beat Marluxia. As you can probably tell, Marluxia is also in the Organization and is in charge of Castle Oblivion. Sora goes to the 13th floor to fight him. Axel comes and fights Sora and fakes his death at the end of the battle. After encountering the Fake Riku again (we see him several times) we proceed to Marluxia. (No, the Fake Riku is not dead, we see him again in Riku's story.
After defeating Marluxia, Namine puts Sora in a strange pod and says that he has to sleep in this to regain his memories to the way they were. She also says that when he wakes up, he won't remember her because the false memories she gave him will be buried within his heart. Sora, Donald, and Goofy accept and go to sleep. This ends with Sora seeing all his friends, and Kairi. He thinks for a second then remembers her name. He the sees Namine, drifting away from him. The Credits Roll. Riku's story is now unlocked.
People, if I missed anything please tell me, and I hope this helps Kairi Forever. I tried to explain it well. If you don't get anything, you can PM me or just ask right here. I'll try and put in Riku's story soon.
I can't get past Axel the second time u fight him