While vampires heal faster than humans, they can easily be killed (and wounded) just like everyone else. It just takes different means to really get rid of them.
Holy objects include crosses and water blessed by a priest. Both will burn them, but not necessarily kill them.
In the series Forever Knight, the main character states "It's a sign of the one true light". Does that also agree with BtVS vampires? A cross and holy water are sacred objects of the Christian faith, but it has not been defined the true reason why they wound (many) demons.
Another reason is simply, it's a universal fact. Almost every vampire movie will say that the undead are hurt by holy objects as they are, after all, creatures of evil.
Same as Holy Objects, the sunlight burns vampires, prolonged exposure (generally less than a minute) will cause them to internally combust. Joss-vampires are allowed to walk in the daylight provided their skin is covered.
Again, it tends to be a universal fact. It connects that creatures that lurk in the shadows would fear the light.
Decapitation immediately kills a vampire.
… They need heads.
Fire will burn a vampire and if not put out, the vampire will go up in flames in a matter of seconds and combust.
"You know what happens to vampires who don't get to feed? Living skeletons, mate. Like famine pictures from those dusty countries, only not half as funny." — Spike, Pangs.
Because vampires need nutrition. Starvation will not kill a vampire.
"I was actually at Woodstock. I fed off a flower person and spent the next six hours watching my hands move." — Spike, School Hard.
Vampires can be "under the influence"; it's been implied that it takes a lot more to drug/inebriate a vampire than it does a human. If a vampire drinks a drugged/inebriated person's blood they will then be affected by the substance.
Because substances like drugs and alcohol go into the bloodstream.
Vampires can be wounded (but not killed) by bullets, knives, angry mobs, hot pokers, and other things that aren't wood going into their body.
They are already dead and are therefore supernatural. They have their own set of rules as to what will kill them.
A wooden stake will only kill a vampire if it goes through their heart.
Again, falling back on the classic mythology of vampirism. In times past dead people (who were buried) who were suspected as being vampires were dug from their coffins and their heart was torn out to see if it was filled with "fresh" blood. If it was, the body was then nailed to the coffin to keep the "vampire" from rising again. That's probably how it came to be that a stake through the heart would kill a vampire.