(Great) Cleave specifies using a standard action, and as per the text you quoted that is valid for Readying an action.
Benefit: As a standard action, you can make a single attack at your full base attack bonus against a foe within reach.
(Improved) Cleaving Finish is a passive effect that procs on any melee attack, so would be valid for a readied attack, supposing you meet the prerequisites of reducing an opponent to 0 up.
Benefit: If you make a melee attack, and your target drops to 0 or fewer hit points as a result of your attack, you can make another melee attack using your highest base attack bonus against another opponent within reach.
Note: I don't think that Improved Cleaving Finish would apply to a readied action attack, but only because I don't see how you'd be able to wreak so much carnage from just one standard!
Cleave Through is, also, a passive effect that procs from a (Great) Cleave attack, so would also be valid if used from a readied action.
Benefit: When using Cleave or Great Cleave, if your initial attack hits, you may take a single 5-foot step as a free action before making your additional attacks.
All emphasis my own.
So long as the attacks you are making all stem from the one standard action, I see no reason why you can't cleave through a horde of enemies: It's not that much different from a Fireball, after all!