How are the Tenchi timelines related? Between Muyo, Universe, GXP, and Ryo-ohki, I'm thoroughly confused. Sometimes Tenchi series seem to be related (Ryo-ohki and Universe) and sometimes not (GXP). What are all the Tenchi series, are they related, and if they are, how?
This is a bit complicated. The links are to MAL, but I've found that different databases index these very differently. Sources are mostly in the links, but I had to reference Wikipedia and Tenchi Muyo Wiki as well.



Tenchi Muyo! Ryo-Ohki is the original OVA series, which was brought to the US simply as Tenchi Muyo (I don't know about other countries). This was adapted into a manga series. Simultaneously the OVA series got a special OVA and then another season. After that there's a special for the second season of the OVA. There's a further third season, which ends the story, and there's a sort of alternate ending special Tenchi Muyo! Ryo-Ohki 3 Plus 1 as well. There's also a sequel manga series which covers some more events, Shin Tenchi Muyo! Ryo-Ohki. Between both manga series, they mostly cover the first two OVA series, and are technically non-canon, though the changes are mostly minor changes.

In addition there are many things in this timeline which are not related to the main story. There's a spinoff manga series about Sasami, Tenchi Muyo! Sasami Stories.  There's also a special for Mihoshi's back-story in this continuity. Tenchi Muyo! GXP also falls in this continuity, 1 year after the ending of the OVA series. The Isekai no Seikishi Monogatari anime takes place 15 years after GXP, and has both a manga and a light novel version. There's also a radio drama (hence no MAL link), Tenchi Muyo! Ryo-ohki Manatsu no Carnival, which presumably falls in this continuity, but I have not listened to it.

The second Tenchi movie, Tenchi Muyo! Manatsu no Eve is sort of separate from everything else. It's technically not placed in the Ryo-Ohki continuity, but a separate, closely-related continuity. Sites disagree on this, but Tenchi Muyo Wiki has the most convincing argument, namely that Kiyone doesn't appear in the Ryo-Ohki continuity, but does in the movie.



Tenchi Universe is on a separate timeline, but is loosely based on the original season of the OVAs. This is a 26-episode TV series. The first film Tenchi Muyo! in Love is a sequel to this series. The third film, Tenchi Muyo! in Love 2 is a sequel to the first film. This film has a manga adaptation.



Tenchi in Tokyo is a 26-episode anime series with its own continuity. The only other things in this continuity are the related specials.



There are a bunch of other spin-offs, mostly with their own continuities. Dual Parallel! Trouble is an alternate continuity, except with mostly different characters. It has a sequel of short episodes. There's also the Pretty Sammy series, which have Sasami as a magical girl and are independent of everything else. There's a 3-episode OVA for Pretty Sammy. There's also a 26-episode TV series with short specials, which in English is known as Magical Project S. This is a different continuity from the original Pretty Sammy OVA series. A third Pretty Sammy series is Sasami: Mahou Shoujo Club, but this is now following Iwakura Sasami, a new character, yet again in an alternate continuity, and it's very much removed from the original Tenchi series. It also has a sequel. Battle Programmer Shirase shares the character of Misao Amano with Pretty Sammy (where she has the alter-ego Pixy Misa), who also makes a cameo in Dual. 

In addition, there's an RPG video game, which is sort-of based on the Ryo-Ohki continuity. There's also an English-language RPG based on the Ryo-Ohki continuity published by Guardians of Order. I have not played either so I don't know how closely they are related to the original series.



To the best of my knowledge, that's everything major that's been released to date. If I've missed anything I'll be happy to add it.