They’re technically undead, which means that just like every other undead they’re animated by dark magic. This is what causes the Light to hurt undead so much; it actively combats their very essence. Not in any malicious way, but because that’s what the Light does— it cleanses tainted things. In this case, that thing would be their body, and it’s just unfortunate for them that it’s also what’s keeping them “alive”:
”[…]the dark magic that sustains them is a buffer that prevents their souls from properly joining with their bodies. This is why undead feel only faint sensations of pain or discomfort from most physical stimuli, and why the Light is so painful to their existence. ” [source]
It wouldn’t take a Naaru’s level of power to destroy them, just a particularly powerful Lightwielder (but a Naaru would certainly do the trick).
If you don’t have the Light at your disposal, the next best method would be to break their runeblade (which you should do even if you have the Light). This is the source of their power. Without it, they would be incapable of effectively fighting back and incapable of regenerating. There are alternating theories on whether or not more powerful (named) vampiric runeblades also consume the soul of their wielder, and if that’s the case, then breaking it may actually release them into death— not unlike a Lich’s phylactery.
If that’s the case, when you destroy their body completely (burn it to ash, for example— they can seemingly regenerate from most injuries, as seen with the Four Horsemen returning even after taking weapons directly to the head) but neglect to destroy their runeblade, their soul might live on inside it and compel whatever unfortunate person that picks it up next to do their bidding.
When they truly die, their soul likely goes to the void, which is described in Sylvanas’ short story. Or maybe they’ll just haunt the shit out of whomever killed them. Who knows.
This explains why I walked away from jumping off Dalaran.