Looking at the rend universal monster ability:
Rend (Ex) If it hits with two or more natural attacks in 1 round, a creature with the rend special attack can cause tremendous damage by latching onto the opponent's body and tearing flesh. This attack deals an additional amount of damage, but no more than once per round. The type of attacks that must hit and the additional damage are included in the creature's description. The additional damage is usually equal to the damage caused by one of the attacks plus 1-1/2 the creature's Strength bonus.
Pretty straightforward. It's treated as a separate attack, so DR applies.
The Rending Claws feat is also pretty straightforward:
Your claw attacks do greater harm to your enemy.
Prerequisites: Str 13, two claw natural weapon attacks, base attack bonus +6.
Benefit: If you hit a creature with two claw attacks in the same turn, the second claw attack deals an additional 1d6 points of damage. This damage is precision damage and is not multiplied on a critical hit. You can use this feat once per round.
The extra damage is added to the second attack as precision damage, so DR is not applied separately.
The Two-Weapon Fighting feat is a bit trickier:
Striking with both of your weapons simultaneously, you can use them to deliver devastating wounds.
Prerequisites: Dex 17, Double Slice, Improved Two-Weapon Fighting, Two-Weapon Fighting, base attack bonus +11.
Benefit: If you hit an opponent with both your primary hand and your off-hand weapon, you deal an additional 1d10 points of damage plus 1-1/2 times your Strength modifier. You can only deal this additional damage once each round.
Based on the description, it works more like the rend universal monster ability, so I'd say that it counts as a separate attack and DR applies.