This character ranking is based on their appearance in Tenchi Muyo Ryo Ohki 1 and 2, Universe and the Universe film trilogy, I may return to this post to add characters and change scores but as of now lets get going.
Tenchi
As far as harem protagonists go, he's the best. The joke is that he's not really needed because he appears seemingly normal compared to his harem but his personality makes the difference in how other characters act. He's strung along a bit but if he were any other harem protagonist then he'd be unlikable.
Ryoko
The term no personal space comes to mind. Her infatuation with Tenchi has never felt natural and usually has to learn the hardway but when she does keep her hormones under control she easily has some of the most powerful emotional moments in the franchise.
Ayeka
I find it difficult to recommend Ayeka as a character because she's not really that much different to Ryoko and lacks many of the traits the quieter part of Ryoko has which makes Ayeka quite a selfish character.
Sasami
Her appearance is little sister at best, token nice kid at worst.
Ryo-Ohki
On par with Pikachu for cutest mascot, but some of the stories she has are not great.
Mihoshi
Gives new meaning to the term dumb blonde and can be unbearable with her ditziness but thanks to her partner in Universe, she has a place she fits into.
Kiyone
And that partner is Kiyone and a character I can easily relate to having to deal with asinine decisions made by clueless people and having no affection for Tenchi gives her the important audience surrogate role alot of harem now lack.
Washu
She's a fun character and has some of the best line reads but like a mary sue, seems to bend the plot to her will far too often. Much of the story plots are started or finished by her.
Yosho
He's fine, it's clear that he messed up alot during his time but if I were to compare him to another character like himself say Genma Saotome from Ranma, I'd say Yosho is only slightly better.
Tenchi: 9.0/10
Ryoko: 8.0/10
Ayeka: 7.6/10
Sasami: 7.5/10
Ryo-Ohki: 7.6/10
Mihoshi: 7.2/10
Kiyone: 9.7/10
Washu: 8.0/10
Yosho: 7.0/10