In the OAV, Sasami is Ayeka's little sister, a mischevious little sprite (okay, that's streching the truth a bit) who is sometimes regarded as the "great manipulator". Going on, Sasami is a greatr chef, and cooks all the time. She has a past entwined with Tsunami, thanks to an accident that almost killed Sasami, and is very quiet and reserved (most of the time). Very attached to Ryo-ohki, we never find out what happened to the fluffy white thing she had as a pet in the first episode of the OAV's. Probably one of the most complex characters in the OAV series.
In Tenchi Universe, Sasami remains esentially the same, except that she has no connection with Tsunami, and her character is pushed to the side. There is one really nice episode with mainly Sasami in it, called "No Need For Ghosts" (I think...)However, Sasami mainly exists as an add-on in this series. There's not much more to say, really.
Here, at least Sasami gets a bigger part (somewhat) than she did in Tenchi Universe. Ryo-ohki is now her pet, and she is still Ayeka's sister (duh). Sasami's part mainly revolves around her friendship with the mysterious Yugi, the misguided villan of Shin Tenchi (Tenchi in Tokyo). Other than that, Sasami is as dull as the rest of the series.