No, you only roll the damage dice of the weapon twice, not any of the modifiers.
This has been cleared up by Jason, and reproduced on the d20pfsrd.com FAQ:
Q: The text of this feat stipulates
that the Vital Strike does not
multiply Strength damage, weapon
ability damage, or precision damage.
Are other damage bonuses (those not
mentioned, such as those from Weapon
Specialization, enhancement bonuses,
or the Bard's inspire courage ability)
are, in fact, multiplied on a hit? I'm
not sure if that's what is intended,
though--the wording sounds like it
could just be saying, "No damage
bonuses, such as X, Y, and Z, are
multiplied on a hit. "
A: (Jason Bulmahn) The way to think
about it is this: roll the damage dice
only twice.
And
Q: So at 6th level and using a
longsword +2 and 16 Str and power
attacking (-2 to hit, +4 damage) using
the Vital Strike feat would it be 2d8,
+2 for the sword bonus, +4 for PA, and +3 for Str or 2d8 +4 for the sword bonus, +8 for PA and +3 for Str? And
then what would the above damage be if
a critical hit was rolled?
A: (Jason Bulmahn) The way to think
about it is this. . roll the damage
dice only twice. Everything else is as
per normal. If you crit, add the crit
damage normally and then roll the base
dice for the weapon again and add them
all together. So, in your example, the
character would roll 1d8+5 attacking
normally, 1d8+9 if using Power Attack,
and 2d8+9 if using Power Attack and
Vital Strike. On a critical hit you
would roll 3d8+10 if attacking
normally, 3d8+18 if using Power Attack
One way to think of this is: resolve the attack and damage normally, then add a weapon-die worth of damage.