1. 공중
means the space between the ground and the sky.
I think it can be at any height from the ground.
ex) 연을 공중으로 날렸다. I flew a kite in the air.
비행기에서 공중으로 뛰어 내렸다. I jumped out of the plane and fell through the air.
2. 허공
means the empty space in the air.
허 refers to 'being empty' and it can be used for both just simple and abstract descriptions.
ex) 허공에 연을 날렸다. I flew a kite in the sky where there is nothing in the air except for it.
하염없이 허공만 바라 보았다. just kept looking at the empty space.
(usually feel empty, depressed, frigtened, disappointed)
3. 창공
means clear and blue sky. I think this is a little poetic, so this can be found lyrics and poems.
So, in a daily life, we just say 파란 하늘, 푸른 하늘.
When I come across this word, the upper part of wide sky with only little bit of clouds comes to mind.
Even though 창 refers to blue, you can use this word for the sky at night as well.
ex)창공에 빛나는 별 twinkle stars in the eather.