Does the Elemental Strike feat from Inner Sea Races get its damage multiplied on a critical hit ? Not sure, as it's energy damage, but not defined by an extra damage die.
I believe it should be multiplied on a critical hit. As far as I know there is no rule that prohibits energy damage from being multiplied just because it is energy damage. The CRB lists precision damage and additional dice from weapon special abilities as the exceptions to the multiplication rule. Elemental Strike is neither.