Limbo is a buffer zone, a dimension between parallel universes, which has served in recent years as a prison. These two were among the most vile of those that resided there, from twin Earths.
Antithesis' origin is unknown, only that he can convert his seemingly alien body into a gaseous form, while possessing mental control abilities. He was the first foe of the Teen Titans, as he manipulated the Justice League versus their sidekicks. It was those kids who vanquished him from a computer database into limbo.
Spirit King's origin likewise is a mystery, although he traced his background to the criminal Roger Romaine, who could de-materialized and mentally control others with his superior will. He was first an adversary of the hero known as Mister Terrific, and years later Terrific's teammate the Flash from the Justice Society. Both champions defeated him, although Romaine manipulated the Flash to slay Terrific on board the Justice League Satelite.
It was when facing twin teams, the League and either the Titans or the Society, that both baddies ended up exiled into Limbo due to their own machinations. Antithesis would employ the crackpot Bromwell Stikk to be his agent, transforming him into Gargoyle to torment their mutual foes in the Titans. As for Roger Romaine, it was an alien entity like Gargoyle that initially empowered him to become the dangerous threat that plagued the heroes of two world.