If the enemy has an immortal 0/5 Otyugh there is only one way to remove it - feed it with a smaller creature.
But then, the Otyugh can often get other creatures.
So I would suggest to make the upped Otyugh to a 1/5 creature and the unupped version to a 1/3 creature.
This way, it can be removed by Fire Shield and Thorn Carpace, before you have creatures out.
Edit: Otyugh is poisoned, when it eats poisonous creatures, now, no need for a 1/5 nerf anymore.