Clerics putting their stake in

question I never thought about: you know Clerics, yes? Generally not happy with the undead.
Can they stake vampires?
The answer depends on the rules you use and how you interpret them.
Basic DnD doesn't say they can't. It bars Clerics from using weapons with an edge. Is a point an edge?
Who knows.
Is a stake a weapon?
Arguably it might be a tool.
I checked Labyrinth Lord and Old School Essentials and both add a ban on pointed weapons, so don't have quite the fidelity they want to have in this question.
ADnD clarifies it in Gygax' overly exacting style, and at the same time makes it worse: it bans edged and pointed weapons (that draw blood)
...
Do vampires actually bleed when you stab them? That opens a whole other can of worms.  Technically your cleric might now be banned from stabbing vampires right after their meal.
You might want to ask first.
Starting from 3.0 the rules don't have any language regarding banned weapons, neither do later rules. It was found to be problematic during playtest.
Does it even matter? Any weapon hitting your face is going to make you bleed, so not having edged weapons is kind of pointless in the first place.