With a two-handed weapon, you add 1-1/2 times your Dexterity bonus on damage rolls, and with an off-hand weapon, you add half your Dexterity bonus on damage rolls. As per the ability's text, if an effect would prevent you from adding your Strength modifier on damage rolls, you don't add your Dexterity modifier. However, any other effects that would increase the multiplier to your Strength bonus on damage rolls (such as the two-handed fighter archetype's overhand chop) do not affect your Dexterity bonus on damage rolls.
