The maneuver Obscuring Shadow Veil does 5d6 damage and is described as a supernatural ability. If I make an attack on a Devil with DR 10/good with a weapon and do 6 damage + 20 damage from the maneuver, does the Devil take 26, 20, or 16 points of damage?
You would deal 26 damage if good; 20 damage if non-good.
A creature with this special quality ignores damage from most weapons and natural attacks. The creature takes normal damage from energy attacks (even non-magical ones), spells, spell-like abilities, and supernatural abilities.
Obscurring Shadow Veil states:
If it hits, your opponent takes normal melee damage plus an extra 5d6 points of damage.
What kind of extra damage are they taking?
the fell energies of the Shadow Hand school.
It helps that they specifically mention "This maneuver is a supernatural ability.'
The maneuver would cause Normal Weapon Damage (that is subject to damage reduction) and Shadow Hand Damage (that is not subject to damage reduction).