I take it your using Messenger Plus! Live.
Simply go to Plus! > Preferences > General > Sounds and untick the ones you want.
If you don't want the song to download, untick 'Automatically download emotion sounds', or if you want them to download, but don't want them to play, just untick 'Automatically play emotion sounds'. Or both?
Also, if you don't want the built-in sounds to play, untick 'Allow build-in sounds to be played'