Language in songs or in speech can cover things like that.

I doubt very much if it actually "don't make no sense"; that is about as plausible as if someone were to say that they couldn't understand "don't make no sense" because it's not "doesn't make any sense".

Write it out in full and it'd be "Last night I dreamed the strangest dream; I never dreamed it before", sure enough. But leaving out the "it" is the kind of thing we do in speech. Grammar and syntax scurry along behind, trying to tidy things up and explain what we do, but they are the servants of language, not its masters.