The paintings predicted that the Kyo'akk Empire would invade the Earth, and provided plans for a super robot, Gekiganger III.
The main characters, and pilots of the titular robot, are Tenku Ken (A reference to Voltes V's sword name), Umitsubame Joe, and Daichi Akira.
The names of the machines are similar to three of the component parts of Combattler V, bringing another 70s mecha anime into the influence on the series.
Finally, Rikuganger is formed with Tank as the head and torso, Jet as the waist and Marine as the legs, and is slow but has great brute strength.
The villains of Gekiganger are the Kyo'akk Empire, an alien race from the "Dark String Universe" (a galaxy shaped like the infinity symbol).
By far the most important plot moment in Gekiganger is the death of Joe, at the hands of Prince Akara's replacement, General Masaka.
The Great General of Darkness, showing pictures of Gekiganger III that children drew, and involves a similar plotline to that movie as well.
As Nadesico progresses, we find that the very reason the Jovians (who are really humans) are attacking Earth is because they believe their cause to be just and that their path is the only true righteous one as they idolize the Gekiganger anime series.
Despite the continuity paradoxes this relationship causes, this episode is apparently canon to Gekiganger, if not to Nadesico, as Akara uses the distortion field again in the movie.