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. After leaving that world behind, he was called back by the force of their will power to save Joan Garrick, wife of Joan Garrick whom the Lord of Limbo captured.
Both Flashs were able to retrieve Joan while also freeing all prisoners of limbo except its lord, with Doctor Fate returning them to their proper space and time. Towards the end of the tale, Fate personally brought Earth-One's Flash back to his world, evidently showing that all aliens were of Earth-Two's universe (in addition to Doctor Fate's previous attempted incursions into Limbo and its Lord's ability to pull in Joan Garrick, as he was unable to pull in someone from Earth-One since it was located in another universe adjacent to but not connected with his own of Earth-Two's realm).
Incidentally, another lord of an adjacent dimension by the name of Ys, this one of Earth-One. who attracted the attention of Hal Jordan and future teammate Zatanna. After defeating their foe, they would face him again alongside the Justice League of America, where despite his own vast array of awesome abilities, he too was vanquished once m ore. It appears these two entities were powerful that they had to be contained in their own parallel prison planes of existence, shuttled off from the two main Earths untold years ago.