QUOTE
Well, my only issue with your question is that I don't remember where it says that Basilisk Venom destroys Horcruxes.
As Triad said as well, it was indeed mentioned. I believe Hermione finds it in one of the books she summoned from Dumbledore's Office. Though she may have come across the information elsewhere, I do not remember. The 7th book does however say that Basilisk Venom and Fiendfyre are capable or destroying a Horcrux.
QUOTE
Even Dumbledore doesn't seem to have a surefire way of destroying them.
It seems that Dumbledore did know how to destroy a Horcrux. If Hermione can obtain that information, then certainly Dumbledore did. This is why he chose to use Godric Gryffindor's sword to destroy the ring, being Goblin-made it
imbibes that which strengthens it, thus taking on the destructive properties of Basilisk Venom.
QUOTE
Which brings up another good question. Are the parts of the soul destoyed, or do they return to the Dark Lord? Anyways, can deal with that somewhere else.
I can answer it quickly. They are destroyed. The only way to make a soul whole again after Horcruxes are made is to feel genuine remorse. Apparently that is excruciatingly painful. But this can only be done BEFORE the Horcruxes are destroyed.
QUOTE
The Killing Curse will kill the Human vessel as you like to call it, but it won't kill the Horcrux. Voldemort would not make Horcruxes if they could be killed by a Killing Curse. He wanted to be immortal remember? He wouldn't be so stupid as to let his immortality hang on such fine threads as hoping that no-one decides to use the AK on his Diary. And since Harry technically died in DH the Horcrux had nothing to shelter it and it perished. And I believe since Harry still had his own Soul he came back.
I disagree, Triad!

I believe it is clear that the Avada Kedavra curse will kill the Horcrux when the vessel is an animate object. When making a living thing a Horcrux, the only suitable place to contain a Horcrux (especially an accidental horcrux) would be the soul itself. The AK curse kills the soul, thus killing the Horcrux. Like I said, we see this in DH. Harry dies as a result of the Killing Curse and thus the Horcrux dies as well, releasing its hold on Harry. Since Harry was tethered to life by his mother's blood in Voldemort, combined with the Deathly Hallows, he was able to come back from the dead- without the Horcrux.
I agree with the notion that the AK would not harm the Ring, the Cup, the Diary, etc. While the AK does destroy inanimate objects, I believe a Horcrux would be impervious to such destruction.