"played on the radio", "played over the radio", "came on the radio" [closed]
They're all appropriate.
Played on the radio.
The above is referring to it being played (or playing) on the radio. It [usually] emphasizes the entity playing the song. "106.7 just played my favorite song on the radio!" OR "They played my favorite song on the radio." OR "My favorite song was played on the radio." It can also emphasize the song, however: "My favorite song is playing on the radio."
Playing over the radio.
The above seems to me to be an older phrase and refers to the song traveling via radio waves. Has the same meaning as "played on the radio".
Came on the radio.
This is the same but emphasizes the song. "My favorite song came on the radio!" It is also in the active voice. The song did something. It came on the radio. The other two are passive voice--something it being done to the song; it is being played.
Referring to your comment above, the following are appropriate:
After the Dentyne ad, Michael Jackson came on the radio.
The radio station played Michael Jackson after the Dentyne ad.
Michael Jackson was played on the radio after the Dentyne ad.
Michael Jackson played on the radio after the Dentyne ad.