DISCLAIMER: I’m not anything like a successful songwriter, and the vast majority of my interest in and experience with writing and performing lyrics involves theatre music. But I think the principles behind lyric writing are pretty constant, so I’ll throw my two cents in anyway.
I agree with a lot of the opinions in this thread in theory; internal rhyme, slant rhyme, and rhymes that use the middle of a word or more than one word are great tools for tightening and improving lyrics. But I also think that avoiding cliches is partly a function of overall approach to writing, rather than a purely technical matter.
Here’s why: I don’t think that cliches are problematic in and of themselves. I think they are problematic because of what they suggest about the song and the ideas behind it. A song filled with cliches isn’t saying anything, and that’s a problem that no amount of tinkering with clever rhymes can fix.
Below are my favorite lyric in the whole world, and my least favorite. Both of them are from songs on essentially the same topic: the singer is in love with someone who is not a suitable mate.
If I could fly,
I’d fly away from you.
Away from it all.
But I am trapped and fighting to break free -
What have you done to me?
I wish I had wings…
No, that’s not true.
If I had wings,
How could I help flying straight to you?
And the other:
Finishing the hat.
How you have to finish the hat.
How you watch the rest of the world from a window
While you finish the hat.
Mapping out a sky…
What you feel like, planning a sky;
What you feel when voices that come through a window go,
Until they distance and die,
Until there’s nothing but sky.
And how you’re always turning back too late
From the grass or the stick or the dog or the light;
How the kind of woman willing to wait’s
Not the kind that you want to find waiting
To return you to the night - dizzy from the height -
Coming from the hat…
So these two passages actually have quite a lot in common. Both use rhyme schemes that aren’t strict ABAB. Both use very simple rhyme pairs, and mostly masculine rhymes (free/me, true/you in the first; sky/die, late/wait in the second).
But the first is filled with cliches. And this is a problem, because the song actually says nothing at all. Who is the singer? What is the problem with the singer’s love interest? From what is the singer trying to “break free?” Almost anyone could sing those words in any situation, and the words would be exactly as appropriate. If you don’t know the stage work that first lyric is from, you wouldn’t be able to guess the context of the song in a million years.
The second lyric is not like that at all. Without me telling you anything about the context, you can probably understand any number of things about the singer, the object of his desire, and the nature of their problem. It is specific; it is saying something unique and personal.
So I think cliche-free songwriting starts with figuring out what your song is trying to say. Write it down. Don’t worry about rhymes, music, meter, or even “writing a song” per se; just write down, plain prose, what you want to say. Now walk away for a few hours. Come back and read what you wrote. Could what you’ve said be just as easily said by anyone in any situation? Then you need to get more specific. “I love you so much” isn’t enough. Why do you love [her or whoever]? Or how does it manifest? Is there a unique behavior? What makes your love for this person unlike all the other loves that have ever been the subject of a song? Were you taken by surprise by someone loving you even though you were closed off (“Head Over Feet”)? Are you so giddy that you feel like you’re actually living someone else’s life (“Wearing Someone Else’s Clothes”)? Are you unwilling to quite admit just yet that what you feel is love, even though it has all the indicators (“Almost Like Being in Love”)?
Once you have something to say that is uniquely yours, the lyric you write will be mostly cliche-free without having to try to make it so.