Episode 6 of the OVA should be mentioned for two things: The introduction of Washu, who destroys two giant snakes who were trying to eat Mihoshi, who inadvertantly freed her, rescues Ayeka from being killed by Kagato, and stands up to Ryoko, while revealing that she's her mom by creation being one. The other being Tenchi's return when he saved Ryoko by chopping off Kagato's hand, plus when he activates the Light-Hawk-Wings for the first time and defeats Kagato in a classic duel sword strike that cuts BOTH Kagato and the ship Soja in half!
Washu is in full badass mode during her whole confrontation with Dr. Clay in the "Zero Ryoko" episode, but it gets even better when, after Dr. Clay has trapped her in some kind of jelly-like material, she breaks free, punches him in the face, and then(even though he dodges it) throws a big-ass chair at him! Dr. Clay abandons ship after that. I would too.
Sasami whipping out a staff and kicking Mishisu's butt was one of the high points of the Third OVA.
Ayeka's reaction after having learned Sasami's story in the OVA. "We love each other. That's what counts."
Pretty much the entirety of the final OVA episode. Z managing to utterly own both Tenchi and Lady Tokimi, Washu and Tsunami performing a Big Damn Heroes to put Tokimi in her place, Ryoko doing whatever it takes to save Tenchi, Tenchi manifesting as a god more powerful than the goddesses AND saving Misaki from her counter-actor state...
Katsuhito is shown holding his own in battle against Kagato in the fifth Tenchi Muyo OVA, even when Kagato had a mind-controlled Ryoko get in on the action. Even got in a cheap attack on the space pirate when he duped him into grabbing Tenchi-ken and feeling its nasty effects.