The "original" plotline is contained in a couple of OAV series and a number of specials. There are quite a number of these Tenchi Muyo videos available for purchase. In fact, so many that I tend to get dizzy and fall over when I see how many that are available. However, I got over it and managed to acquire everything short of the first Pretty Sammy volume.
The DragonBard was kind enough to provide a brief summary of the OAV series:
In the OAV series, Ryoko was the one who was imprisoned over 700 years ago, and at the beginning of the series Tenchi accidentally frees her. Then Ayeka and Sasami show up looking for their older half brother, who was the warrior that imprisoned Ryoko. Ryoko and Ayeka both fall for Tenchi. Kain, a villain from Ryoko's past shows up with Mihoshi on his tale. They all get captured, Mihoshi accidentally frees Washu. At this point, Tenchi and his grandfather, who happens to be the long lost half-brother, beat up Kain and go home, leaving Tenchi with three attractive young women who want him.
Except that in the first OAV series, Kain [the nasty from the movie] is Kagato, I would also add that the OAV series has more adult situations then the T.V. series, especially the The Night Before The Carnival special.
Tenchi Muyo Ryo-ohki - OAV series 1
Tenchi Muyo Ryo-ohki - The Night Before The Carnival [Episode #7]
Tenchi Muyo - Mihoshi Special
Tenchi Muyo Ryo-ohki - OAV series 2
The Tenchi Universe - Tenchi T.V.
Tenchi Muyo: The Movie
Tenchi & Friends Special: Pretty Sammy 2