Literally "in the air" means something suspended in the air. And the word "up" is usually used with it.
For example,
"we saw the plane flying high up in the air".
But as an idiom, it means, in circulation, in people's thoughts.
For example,
"There's a rumor in the air that they're closing".
"Christmas is in the air".
" Though speakest,
but,
thy words are in the air".
On air, or on the air means "broadcasting or being broadcast".
For example,
"The program will be on air at 3:00 PM:.
"He changed his on-air name".