Omni

The active player may trigger any ”Omni:“ abilities under their control during any of their turns, even if the card with the ”Omni:“ ability does not belong to the active house. When a player uses a creature to trigger its “Omni:” ability, the player exhausts the creature and then resolves that “Omni:” ability

—Official rules v1.8 March 2021

FFG Rulings

• I have a stunned Saurian Egg in play. I have chosen a non-Saurian house this turn. Can I use Saurian Egg's Omni: ability to remove the Stun?
  Yes, an Omni: ability lets you use the creature outside of the Active house, which will allow you to remove the Stun from the creature.

  Source: Crucible Cast 25

I have a stunned Saurian Egg in play. I have chosen a non-Saurian house this turn. Can I use Saurian Egg's Omni: ability to remove the Stun?

Yes, an Omni: ability lets you use the creature outside of the Active house, which will allow you to remove the Stun from the creature.

Source: Crucible Cast 25