In our last campaign we were fighting a medusa with our eyes averted. With that blinded condition, can I cast an area of effect spell on the space that a medusa is standing in without looking at the medusa itself?
If you avert your eyes from the Medusa, you still know where she is, but you do not actually see her.
You can still hear her voice/movement/breath etc. unless she hides from you. Thus you have a good idea where she is, but you are not actually seeing her so you are attacking an unseen target (PHB p.194f), which should be irrelevant for most area of effect spells.
Knowing where she is, you can cast an area of effect spell on the Medusa. If the spell has to be cast 'at a point you can see' you must see this point, thus you would have to choose a point next to the Medusa, so you can avoid looking directly at her.
If she hides from you (which is possible when you avert your eyes) you would have to guess her location and cast the spell at a point of your choice, hoping she is in the area, but there is no guarantee that you hit.
You can target by sound. You will still have disadvantage on the roll though. If they are hiding (using the stealth skill to remain unseen and unheard) you will have to guess or use special skills or senses to pinpoint their location.
PHB p194 (Emphasis Mine)
When you attack a target that you can’t see, you have disadvantage on the attack roll. This is true whether you’re guessing the target’s location or you’re targeting a creature you can hear but not see.
This would also allow you to center an area spell so that it would include the medusa.