Odan was a person of unknown species. He declared he was a Trill, but he didn't look like one. Jean-Luc Picard stated that he looked either like a Romulan without pointy ears or like a Klingon affected by the augment virus, so he most probable was one of these two.
Odan visited the Enterprise to start a love affair with Beverly Crusher. He came very close to get on with her, but the jealous Jean-Luc, who wanted to nail Beverly since they had met first time, killed him while he was away in a shuttle and made it look like an attack of some aliens. This was no big thing to Jean-Luc, he had also killed Beverly's first husband to have better chances after helping her to get over that "tragedy". (TNG: "I know what you are thinking...")
Due to Jean-Luc's bad luck, Odan was a more freaky alien than everybody had thought. He survived the attack by leaving the dead body and occupying the body of Will Riker. With the abilities of this chick terminator it was easy for Odan to succeed. Picard even planed the next murder when Odan made a big mistake. After wondering about the question "What is better than hot sex with a girl?" for a long time he finally got the answer: "Hot girl-on-girl-sex!". So he ordered his female backup-body to go on board the Enterprise and switched bodies again leaving Riker's and entering the girl's. (By the way, this was the only thing that saved Riker's life. Picard would have killed him without hesitation, because who needs a Number One that is only interested in scoring with chicks, even if this means to destroy the ship for some "nice fireworks".)
But Odan's plan didn't work, because Beverly was not interested in having hot sex with another girl other than Deanna Troi, or Tasha Yar, or Ro Laren, or... Anyway, she was not interested in that girl. Odan got kicked out of the airlock by Picard, and the episode ended. (TNG: "This freak pretends to be a Trill? I don't think so!")