For me, I suppose it varies creature to creature, and campaign to campaign.
Elementals have a sort of "heart" (like your "energy core", I imagine?) that's disruptable. The heart is effectively their spiritual connection to their plane, and harming it threatens the integrity of the creature's body.
Fire beings specifically could also be "worn" down as weapons absorb a bit of the creatures' essential heat. (Of course, this means the weapons heat up a bit, too.) Cold, windy creatures might suffer the opposite effect, warming up little by little with watch hit.
Ethereal beings I ususally envision as being harmed by the ethereal "shadows" of weapons. Slashes manifest as rips that "leak" a bit of essence that evaporates, while bludgeons could manifest as wavery or ripply impacts.
Shadow creatures are harmed less by the weapons themselves, and more by any light admitted when a weapon hits. The impact temporarily opens a hole allowing ambient light to burn the creature's innards.