What would have happened if Neville had used a normal sword to chop Nagini's head off?

Yes, but how much would he have hurt her? Would he have been able to hurt her enough to put her out of commission?

I wouldn't think so. Think about how the necklace reacted to other magic, it only jumped away or flew a few feet in the air. I assume the same would happen for Nagini.

Yes but the necklace wasn't a living thing

But Harry was also a horcrux and he got hurt all the time. Eg broken arm in quiddich, scar on hand by Umbrige's quill, almost drowned in lake, cut himself, etc,etc

Hurt, not dead. Hence the term the boy who lived.

@ limits: I know that, that's why I asked the question. We know that normal sharp objects can damage a living horcrux as evidenced by Harry cutting his hand on a mirror. So my question was what would happen to Nagini had Neville cut it's head off with a normal sword. Woul the head grow back?

I thought the avada curse worked which is why it killed the horcrux in Harry when Voldemort cast it on Harry in the Forbidden Forest

good point, but maybe thats because harry was human.

Not so much human as living. You can destroy a horcrux by causing it damage that can not be reversible by magic. I assumed the avada can not break or cause physical damage to an inanimate object and that's why it wouldn't work on a not living horcrux.

Hmm, if Voldemort put a charm stopping sharp things from cutting or piercing through Naggini, then the sword of Griffindor would not have had any effect on Nagini as it's the basilisk poison imbued in the sword that makes it deadly to the horcrux. If the sword can't pierce the skin then the poison in the sword wouldn't be able to enter the snake's body. We know that mere contact with a weapon imbued with the poison is not enough to kill anyone as Hermione handled a basilisk fng and did not die from coming in contact with it.