Gekiganger 3

A Show Within a Show to Martian Successor Nadesico, Gekiganger 3 is an affectionate pastiche of Super Robot anime of the 1970s and 1980s. An OVA was released in 1998 which compiled all the Gekiganger 3 clips seen in Nadesico in chronological order and included a Short Anime Movie.

The ancient Super-Paleolithic people predicted that the alien Kyo'akk empire would invade the planet and left behind plans for a Super Robot, Gekiganger III, to stop them. Professor Kokubunji builds it, and Hot-Blooded pilots Ken Tenku, Joe Umitsubame, and Akira Daichi take it into battle against the mecha monsters of Prince Akara and his overlord, Emperor Hyperion. Midway through the series, Joe is killed and the Gekiganger III is destroyed only to be replaced with Gekiganger V and new pilot Tetsuya Ryuuzaki.

Sounds exactly like every other Super Robot series out there, right? Good, that's the point.

The OVA movie (with the Framing Device of the Nadesico cast seeing the movie in a theater) features the return of the Super-Paleolithic people, who attack both the humans and the Kyo'akks in an attempt to reclaim the world. Akara must temporarily join forces with the Gekiganger team to stop them.

Title completeness aside, not to be confused with Juken Sentai Gekiranger.

This Show Within a Show includes examples of:

Affectionate Parody
Alien Invasion
Aliens and Monsters
Aliens Steal Cable: The Kyo'akks research Earth culture by watching anime.
All There in the Manual We only see short clips of the series in Nadesico, but there's plenty of supplemental material included with the merchandise that tells more of the Gekiganger story.
Americans Are Cowboys: Cowboy Johnny and the Texas Robo.
Amnesiac Dissonance: Aquamarine, an enemy who gets amnesia in a crash and falls in love with Ken.
Back from the Dead: Joe Umitsubame of course.
By the Power of Greyskull
Calling Your Attacks: It's a Super Robot show, what do you expect? GEKIGAN SWORD!
Chest Blaster: GEKIGAN FIRE! Only on Gekiganger V curiously enough.
Combining Mecha
Days of Future Past: Despite being a perfect imitation of a 1970s super robot show, it was supposedly created in the 2090s.
Defictionalization: Not only is there a real OVA, there's also plenty of real-world merchandise, including soundtracks and a replica of the action figures seen in Nadesico. One collector's edition of Nadesico even comes with a Gekiganger fanbook.
Deflector Shields: Both Akara's robot and the Kokubunji lab have them, the former of which was, oddly enough, based on the Nadesico's Distortion Field. A strange result of the Clip Show episode causing a recursive case of Show Within a Show.
Eagle Land Cowboy Johnny and his Texas Robo.
Excited Episode Title: Parodying the infamous Mazinger Z example.
Expy: The main cast are all Expies of the cast of both Getter Robo and Voltes V.
Eye Beams: GEKIGAN BEAM!
Face Heel Turn: Nanako's brother Rokuro becomes a villain.
Finishing Move: GEKIGAN FLARE! And... DOUBLE GEKIGAN SPARK! Both of these include the "you have to get this just right or you'll blow up" speech before they're used.
Five-Man Band: Ken, Joe, Akira, Junpei, Nanako.
Fully-Absorbed Finale: Not exactly a "finale", but the OVA actually does advance the story of Nadesico briefly, by showing that Akito and Yurika are going to get married.
Heroic Sacrifice: Joe, Sapphire, and Aquamarine.
Hot-Blooded: CHOU-NEKKETSU-GIRI!
Humongous Mecha: Affectionately pastiched.
Inescapable Net: GEKIGAN NETTO!
Lost Technology
Mad Scientist's Beautiful Daughter (Nanako Kokubunji)
Meaningful Name: See Theme Naming below. Also, Ken Tenkuu's name when said in the proper Japanese order of Family -> Given, is rendered as Tenkuu Ken, which was the name of the weapon used to execute Voltes V's Finishing Move.
Mecha Expansion Pack: Spaceganger and Dragonganger
Mecha-Mooks
Monster of the Week: Presumably... we don't see Gekiganger every week.
Mid-Season Upgrade: Gekiganger V
Narm: Intentional, as part of the Affectionate Parody. Even In-Universe some people comment on how ridiculously melodramatic the plots can get.
No Export for You: For a while, the OVA was the only animated Nadesico-related material that didn't get licensed, however Nozomi Entertainment licensed it along with the Nadesico series and movie in 2011.
Off-Model: Again, intentional, though there's surprisingly little of it... the biggest offenders are probably the fight scene between Ken and Joe, though that's more of an Art Shift, and Joe's mouth when he's telling Ken to use Gekigan Flare before he dies.
Power Trio: See the FMB above and subtract Junpei and Nanako.
Recap Episode: The Gekiganger team watches the Recap Episode of Nadesico.
Retraux
Rocket Punch: GEKIGAN PUNCH!
Say My Name: "JOOOOOEEEEEEE!!!" is the most famous, but there's also "SAPPHAIAAAAAAA!", "AQUAMARIIIIIINE!" and even, in the movie, "KEEEEN!"
Shout-Out: If it's not foreshadowing for the plot of Nadesico, it's probably a Shout-Out to an old-school anime: see below.
Show Within a Show: Martian Successor Nadesico. It runs both ways. Don't try to figure out how that works.
- Why not try?
Stay in the Kitchen: Done only slightly less obviously than usual in the movie- Nanako wants to replace Ken in the Gekiga Jet but Joe tells her she should stay with him instead. Despite this, the Jovians in Nadesico who based their culture on Gekiganger follow this as a philosophy.
Theme Naming: The family names of the main pilots have to do with where their vehicles run. Also, Aquamarine and Sapphire are both named after jewels and both fall in love with a hero.
Title Theme Tune
Transforming Mecha

Anime series that receive a Shout-Out in Gekiganger 3 include:

Combattler V and Voltes V: The villains are similar to those of these series; Gekiga Jet, Marine, Tank = Combattler V's Battle Jet, Marine, Tank; Gekiganger V's name comes from Combattler V and upon its appearance performs the same pose; Gekigan Sword = Voltes V's Tenkuu Ken, which also gave its name to Gekiganger's hero. And "Let's Gekiga In" is a play on Voltes V's "Let's Volt In".
Daitarn 3: the logo for the show is very similar in the design for the "3"
Devilman: Gekigan Cutter = Devil Cutter.
Getter Robo: the three-machine/three-robot system; the character archetypes of the pilots and supporters; Gekigan Vision = Getter Vision; one of Rikuganger's finishing moves is named for Musashi; the death and replacement of a main character (though not the same archetype); the final pose in Gekiganger's transformation sequence is the same as that of Getter Robo G; Cowboy Johnny/Texas Robo = Jack King/Texas Mack.
Mazinger Z: Gekigan Fire, Gekigan Punch, Gekigan Beam = Breast Fire, Rocket Punch, Koshiryoku / Photo-Atomic Beam; "Gekiganger Dies In Flames!" = "Kouji Kabuto Dies In Lava!"; The movie has a similar plot to one of the Mazinger Z movies and begins with a similar opening sequence. The Gekigan Sword is also deployed from the side of the knee, just like the Mazinger Blades. Joe's Big Damn Heroes moment at the end of the series is similar to Tetsuya and Great Mazinger's introduction in the Mazinger Z movie as well.
- Great Mazinger and Daimos: The Sixth Ranger Tetsuya Ryuuzaki is named after the main characters of Great Mazinger (Tetsuya Tsurugi) and Daimos (Kazuya Ryuuzaki).
Science Ninja Team Gatchaman: The Hero and The Lancer are Ken and Joe, respectively. And Joe dies and returns...