Cliché is the most commonly used of these three words in American English. It's come to refer to a phrase or idea that has been encountered too often and is thus both unoriginal and unsatisfactory. A cliché-ridden speech will bore its listeners. A cliché ending to a story may disappoint an audience (though, if the genre is romantic comedy, it may well be exactly what the audience is looking for).
Of the other two words, trite is closest in meaning to cliché. It is generally used to refer to something that feels worn-out and dull, which accords with its root in the Latin verb meaning to rub/wear down.
The biggest difference I've observed between cliché and trite, aside from the fact that the latter is slightly less common, is that people periodically use trite as a synonym for boring or vapid, even if the subject hasn't specifically been encountered before. (This isn't correct, per se - something trite has, by definition, been encountered excessively - but it does occur.)
Additionally, things described as cliché are often intended to be sweet or sentimental and end up saccharine; things described as trite were more likely intended to be sincere and deep and end up sounding hollow.
Passé is rather different from these two words. A fair synonym is dated - something that was once fashionable (perhaps even quite recently), but no longer is. While phrases, images and ideas are often described as cliché or trite, the word passé is more often used to describe objects, fads or fashions. A story's ending would not be described as passé; heroin, on the other hand, might be.