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A very common occurance, a Paladin has used Sign of Vulnerability to apply Vulnerable 5 Radiant to an enemy.

In the following round, they use the Minor Action, Bless Weapon, which adds 1d6 radiant to the next attack with the weapon, followed by Strike of Hope, which, for simplicity, we'll say does 1d6 Radiant. In the same round, they activate as a free action, Holy Smite, adding 9 Radiant Damage.

Examples, which assume the 1d6 attacks all deal 6 damage:

1: Each ability, while used in a single attack, has its own damage sequence, and the target takes 6 from the Strike, 6 from the Blessed Weapon, and 9 from the Smite, and each gains its own +5 radiant damage, for a total of 36 radiant damage.

2: Though they are all separate abilities, it is one instance of the combined attack, and the vulnerability is only applied once, for a total of 26 damage.

3: Bless weapon specifies that it is "Extra radiant damage" not "Takes radiant damage", so it does not benefit from its own damage sequence, and is looped in with the Strike, but Holy Smite declares its own attack, and two vulnerability damages are applied for a total of 31 damage.

My intuition tells me that 3 is most syntactically correct, while 1 is most functionally correct, as each ability is spent equally, they all get the full benefit of effects. 2 seems unlikely, but still makes sense, as it is a single swing of the weapon to trigger damage.

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A creature vulnerable to radiant damage would take 31 damage in this case.

Your #3 is the correct answer.

Bless WeaponDDI deals Extra Damage which does not trigger separately. Indeed, you need to deal damage with your attack or Bless Weapon won't deal damage at all. Normally you don't have to hit with your triggering attack, only deal damage for to add the extra, however Bless Weapon overrides that and specifies a hit is needed.

Extra Damage snippet from DDI:

Extra damage is always in addition to other damage.

Holy Smite triggers when you declare a target for Strike of Hope and therefore gets the benefit of the radiant damage separately.

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