The Omega Men were a team of rebels hailing from the Vegan planetary system, consisting of twenty-five habitable planets, which had een ruled for millenia by the Citadelians. These freedom fighters journeyed to Earth-One and joined forces with Green Lantern, Superman, and the New Teen Titans. During the Crisis on Infinite Earths, these Omega Men protected their own solar system while continuing their fight against their alien overlords. At that time, they had not liberated all worlds there.
Earth-Two's Doctor Fate stumbled upon several exiles from his own universe of Earth-Two, all enslaved for untold centuries in a limbo dimension by a powerful lord seeking company in his own imprisonment. During one adventure through time and space, Earth-One's Flash vibrated as he often does yet instead of being pulled into Fate's universe it was Fate's adjacent dimension wherein the Fastest Man Alive met this assortment of aliens. Flash would return with his counterpart in order to save that hero's wife Joan Garrick, whom the self-styled Lord of Limbo had pulled to his reality. This paralleled the action in Earth-One's universe of the alien Golden Man, who claimed his universe's Flash and then Kid Flash along with the Earth-Two version. Like the Limbo Lord, the Golden Man was the sole occupant of his world and sought help from the Fastest Men Alive to free him.
Incidentally, other evil entities of adjacent dimensions in Warlock and Azmodus caused trouble simultaneously on parallel planes of existence, the former battling Green Lantern and Zatanna of Earth-One and the latter quarreling with the Spectre of Earth-Two. Each attempted to assert control in dimensions other than their own, yet each ended up immobilized at the exact same time by their foes.