My friend Molly is also an avid Harry Potter follower, and she posed a rather vexing question to me. It went something like this:
"If Harry is a Horcrux, then technically he should have been indestructible to all harm from the moment he became one and the only way that Voldemort could have killed him was either by stabbing him with the fang or the sword or with fiendfyre. Conversely, in the Chamber of Secrets being bitten by the Basilisk should have killed the horcrux inside him, even if Fawkes brought him back to life...What say you good sir?"
Molly, a great and perplexing question. It is a mystery, wrapped in an enigma. Allow me to attempt to answer your question, and see if you like what I'm throwing at you.
I will try and address each part of what you stated or asked. First, a part of Voldy's soul is indeed inside of Harry. However, I would not go as far as to say that would make him indestructable from harm. In fact, it would simply make Voldemort (theoretically) indestructible. Here is what I mean. Voldy has part of his soul float into Harry. This means that you cannot totally kill Voldemort until HArry is dead. Now, that piece of Voldemort's soul doesn't make Harry any more impervious to harm or to death. Nothing about having a horcrux inside you makes you stronger, or your soul any stronger. Now, if a piece of Harry's soul would have flitted back into Voldemort, then it is possible that your logic would be correct. So basically, Harry wasn't protected from dying any more than anybody else. Being a horcrux is actually the absolute crap end of a magical deal. You hold someone's soul and they basically get really strong and then try to take over the wizarding world. It's basically like being a bartender, and trying to tell Charlie Sheen it's last call....Nobody wins in that situation.
Now, onto the second part of the question. You mention the different things that could have killed the horcrux inside of Harry. Now my logic could be completely wrong, but let's give it a shot. I think Harry could have been killed in any normal way. Normal, of course, is a relative term in the wizarding world; but as wizards go I think conventional methods would have done the job. Here is why. To destroy a horcrux you have to damage it beyond magical repair. So, in order to destroy Harry (or the part of Voldemort's soul that was inside of Harry) you would have had to damage the magical object (Harry's Body) beyond all magical repair. Avada Kedavra would have done just that. Seeing as how there is no way to bring people back from the dead (ghosts and priori incantatum people withstanding), killing Harry via magic would have destroyed his body beyond all magical repair, thus killing the horcrux inside of Harry. Since Harry did not die, I think that is the reason why the horcrux inside him was not killed, he wasn't damaged beyond magical repair.
I base my argument on this idea. However, I do admit there is evidence that makes what I think a little murky., When we first learn about the dementors, we are introduced to the idea that you can live without your soul. In fact, in the books they say "you can live without your soul, you know, as long as your brain and heart are still working. But you will have no sense of self anymore, no memory, no...anything. There is no chance at all of recovery. You'll just exist, as an empty shell." I think that this means that the opposite would not hold true. If your physical body dies your soul dies, but your soul can die without your physical body dying. So although Harry's soul could have died without him dying, I still think destroying a horcrux is all about damage beyond the realm of repair.
I think of this much like this. Imagine Harry is in the Chamber of Secrets and instead of stabbing the diary, he rips out a couple of pages and stabs those. Though he would have injured the vessel that the soul was housed in, he would not have destroyed it beyond magical repair, and thus that part of Voldemort's soul would have continued to exist. Now, if Harry would have died in the chamber, than the horcrux would have died, and at that point I think any old wizard could have finished off Voldemort.
That's my story, and I'm sticking to it! Let me know what you think...
MLH