According to ancient legends and even regarded as sacred by Li Mei's people, it was believed to be a portal to The Heavens, left behind by the gods and sealed away in an ancient stone structure within an old tomb in Outworld.
Thousands of years later, after the Deadly Alliance took over Outworld, they discovered that the tomb they located on a nearby plateau outside a small Outworld village, contained the relic within it. They forcibly ordered its citizens to build a palace around it. In return for help resurrecting the mummified army of the Dragon King, Quan Chi used his magic to unlock the mystical vortex from the stone structure. Countless dead souls and spirits appeared in the skies and spewed forth into the Soulnado from all over Outworld.
Shang Tsung tapped into the Soulnado and gained a vast amount of souls and power. Consequently, he felt his youth and power returning to him like never before. Ultimately he obtained access to so many souls that he could sustain himself forever. The energy from the Soulnado was also used to fully resurrect Onaga's armies. This essentially confirms that the legends from Li Mei's people were indeed accurate.
When Onaga returned to Outworld, the two sorcerers allied themselves with Raiden out of desperation. Their combined might however was still not enough to defeat Onaga. Raiden was eventually forced to use up his godlike essence in order to create an ethereal blast. Whilst this blast was powerful enough to destroy the resurrected army and the palace itself, it had little effect upon Onaga due to the fact Onaga held the last Kamidogu (the stolen Amulet of Shinnok). The Soulnado vanished as the portal to the heavens closed. All the trapped souls were separated and set free.
The ninja known as Scorpion was almost torn apart by the Soulnado after he was thrown in there by the two Oni Drahmin and Moloch. Fortunately for the ninja, he was saved by the Elder Gods and transported to the void.
In Mortal Kombat (2011), Quan Chi used an incantation and opened up a Soulnado in a graveyard in Earthrealm to allow Shao Kahn to take all of Earth's souls. The ritual involved sacrificing a number of human soldiers. Its opening was witnessed by Cyber Sub-Zero and it was closed when Nightwolf threw Noob Saibot into it.
The Soul Chamber in Shao Kahn's Fortress also seems to contain a Soulnado, albeit a small-scale one. It is where the gestalt warrior Ermac was created and appears to be his "home" where he recharges. This particular Soulnado was likely made by Kahn himself (or possibly Shang Tsung) with the many Souls of his vanquished enemies.
Shang Tsung summons a Soulnado in one of each of his intros and outros in Mortal Kombat 11.