The Varia (as they are apparently called) are the villainous force from Syvalion. This mysterious alien race is plotting an invasion to Earth, abducting humans to be converted into robotic slaves. They are mutants with no shape of their own, being able to manifest out of thin air and possess human bodies.
Since the story of the game is played in a scenario system, every time you play the story is played differently, always revealing a small portion of the general plot. In most scenarios the unnamed hero steals the Syvalion ship from the aliens to fight them. As it turns out, they were actually humans who were bio-engineered by scientists, but ended forgotten on another planet, where they evolved and plotted their revenge. In one of the scenarios, the hero meets with a pale old scientist, who was apparently one of their creators, trying to create a super intelligent being.
In most endings (the game is said to have about 100) the hero thwarts the alien's schemes, but in some he fails to stop the invasion or is killed by them. While the hero's fate is unknown, the Syvalion ship have been somehow stolen by the Belser, who later converted it into the Dark Helios battleship.