Which is the appropriate way to proceed if I want the following to happen:

The player has a unique weapon (which can be given a unique enchantment if that is needed) and he/she is supposed to attack an activator with this. This should trigger a scripted event.

Can weapon strikes be detected on activators? Where should the script be placed?
I really have no experience with this sort of scripting, so any help is appreciated.

Perhaps the http://www.creationkit.com/OnHit_-_ObjectReference event would work? The script would have to be attached to the activator.

I haven't used it before, but it looks like it should give you all the necessary information needed to detect what the activator was hit by.