Hypersmurf
Moderatarrrrh...
Jhulae said:Except the FAQ isn't wrong.
"An unarmed strike is always considered light, as is an off-hand attack with a double weapon." (RC, page 148)
It sounds like they've cleaned up the ambiguity, then, removing the potential for two different readings - up until a couple of weeks ago, it could be read in different ways

So, with regard to the OP's question: You have to take the penalties to get your Dex modifier on the off-hand attacks with a double weapon, since it wouldn't be an off-hand attack without using TWF.
Unless they've changed the definition of off-hand in the Rules Compendium as well, your off-hand is your weaker or less-dextrous hand (usually the left) according to the PHB - so you can make an off-hand attack with a single weapon, if it's held in your weaker or less-dextrous hand (usually the left).
Of course, since a double weapon is held in both hands (unless, perhaps, you're a Large creature with a Medium quarterstaff held in your off-hand), you generally wouldn't make an off-hand attack with it unless using both ends. Except...
According to the FAQ's take on greatsword and armor spikes, for example, it's also conceivable one could make a primary attack with armor spikes and an off-hand attack with a greatsword; similarly, one could also make a primary attack with armor spikes and an off-hand attack with a two-bladed sword held in both hands. Per that Rules Compendium quote, it would appear that this off-hand attack would mean the two-bladed sword (a double weapon) would be considered a light weapon.
-Hyp.