For convenience, this list of Music has been divided into Songs, which could be listened to, in real life, in Improbable form, and Lyrical Poems which could not be.1)2)
Simple test: could you include the song on an “Improbable Island” mixtape, then give said mixtape to an off-island friend and enjoy their confusion at the lyrics about cats and Improbability Drives and Mutants? If so, it goes in “Songs”. If not, it goes in “Lyrical Poems”.
Please make sure that your hypothetical friend is actually confused by the lyrics about the Island, not just by the fact that you've handed them a cassette tape.