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.
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.
There are 3 major timelines in Tenchi Muyo!. There is the OVA/Ryo-ohki timeline, the Universe timeline, and the Tokyo timeline.
The OVA/Ryo-ohki timeline is the original timeline released, and is considered the primary canon story. It contains 3 OVAs and 2 OVA specials (which make up 26 episodes of Tenchi Muyo!, the one that aired in America). Also in this timeline is Tenchi Muyo! GXP, and the newer series, Tenchi Muyo! War on Geminar.
The Universe timeline consists mainly of Tenchi Muyo! Universe which began as a story based off of the first 6 episodes (the first OVA) of the Ryo-ohki timeline. However, it branched into it's own story, and got two movies, Tenchi Muyo! Tenchi in Love and Tenchi Muyo! Tenchi in Love 2, also known as Tenchi Forever!.
The final major timeline is the Tokyo timeline, which is where the series Tenchi in Tokyo! fits in. It is really on it's own there, but was originally planned to be an extension on the Universe timeline[source]
From there, there are a few spin off timelines. The first and still sort of canon one is the Pretty Sasami timeline, which has many ties to original characters from the series. Note that each of the series in the Pretty Sasami timeline is very related, but in its own continuity. And then there are non-canon ones like Sasami: Magical Girls Club.
Overall, this is a series that has a lot of conflicting canon without really having anything set.