Stinging Study
I wonder if it works with Awaken the Blood Avatar or if it only counts the Extus, Oriq Overlord portion.
Stinging Study does not specify that the Commander must be a commander creature. Commander-ness is a trait of the card. Not the creature. Hence, the commander tax will apply to Extus or Awaken regardless of which side you are casting now and regardless of which side you have cast previously.
So, if the card is in the command zone, you can choose either side.
But, only Extus exists on the battlefield. If Extus is on the battlefield, Awaken the Blood Avatar does not exist anywhere.
Bottomline: Commander in the command zone, you can choose either side. Commander on the battlefield, you can only choose the current face-up side.