Yeah, as Reaver points out, the list of Elemental effects never mentions an AP value, with the exception of Fire. And Fire only mentions that the test to resist catching on fire applies the "Fire AP" as a penalty also. Even so, elemental strike doesn't have a Force and it isn't a "fire-based weapon" (which would be referring to things like flamethrowers).
Personally, I interpret the power as applying this:
Acid: -1 Armor for each hit.
Cold: Armor might break (single hit on a Simple Armor Test avoids)
Electricity: -5 Initiative, -1 on actions for 1 Combat Turn.
Fire: Might catch on fire (Armor must make net hits from attack to avoid)
Water: Target can get knocked down (Agility test to reduce original damage below Physical Limit)
* A few notes, I make note that Acid only reduces the Armor by 1, not a progressive -1 every combat turn. I say this because the assumption of the Acid damage seems like it is intended to be something like throwing a vial of acid at somebody, the Acid continues to eat away at the surface. When it is a physical attack, you aren't leaving the "Acid" on the target, so it doesn't remain to eat away the armor. Ant Spirits (SG pg 95), have a similar effect, they are considered to have their attacks be considered Acid.
Fire, likewise makes mention of a "Fire AP" I would probably be willing to apply the Adept's Magic as the "Force" for this purpose, or else just use a flat -2 for open flame level fire.