I started out thinking that IanB's interpretation is correct, but I think I'm coming around to Dlichen's interpretation.
Let me see if I can explain why... in a roundabout way:
Two-Weapon Fighting
Heroic Tier
PreRequisite: Dex 13
Benefit: While holding a melee weapon in each hand, you gain a +1 bonus to damage rolls with your main weapon.
When I read this I see that it does not refer to wielding the offhand weapon. Therefore, by RAW, you should still get the TWF bonus even if you are not capable of wielding the weapon you are holding in your offhand. For instance, if you are using a light shield, you can hold a weapon in your off-hand, but not attack with it. If you do so, and you have the Two-Weapon Fighting feat, then by RAW you should get the +1 damage bonus.
Two-Weapon Defense
Heroic Tier
PreRequisite: Dex 13, Two-Weapon Fighting
Benefit: While holding a melee weapon in each hand, you gain a +1 shield bonus to AC and Reflex.
By RAW, again, you can hold a melee weapon in your offhand and gain a bonus from it even if you are incapable of wielding it.
Two-Weapon Flurry
Epic Tier
PreRequisite: Dex 19, Two-Weapon Fighting
Benefit: While holding a melee weapon in each hand, if you make a successful opportunity attack with your primary weapon, you can also make an opportunity attack with your off-hand weapon against the same target (but with a –5 penalty to the attack roll).
Now... this one is trickier... I can interpret it as a case of exception based design, however. The specific (this feat) overrides the general (you can't attack with a weapon you are merely holding and not wielding). So yeah, again by RAW this feat will allow you to attack with a weapon you are holding in your shield hand. Probably...
Those interpretations, however, are undoubtedly counter to the intent. TWD is intended to be a replacement for a shield, not an additional benefit for shield users. I think they probably meant to say "wielding", not "holding".
But here's the really sticky bit with that interpretation. If the TWF feat said "wielding" instead, then by RAW DLichen would unarguably be correct. If you had the TWF feat and you attacked with your main hand, then you would be wielding both weapons as part of that attack. This might even be the intent, because - let's face it - that +1 damage is coming from the fact that you are also poking them with your dagger in addition to the sword. And letting Rogues use their powers with longswords seems to be far less stupid than letting all of the above nonsense work.