'sound' is any kind of noise or vibration through the air capable of being heard.
'audio' always relates to a recording of sound of some sort.
'volume' is the level of this sound or audio.
"The sound was very soft on the audio tape, so I had to turn up the volume."
"The sound of my dog's bark was very strange. I decided to make an audio of this sound. I had to do it twice because the first time the volume on the audio recording was too low."