Damage of multiple damage types still only do one instance of damage. However, it is counted as the nastiest type of these in case the monster has any resistances or vulnerabilities.
Let's say your Starlock has some sort of Chill of the Stars power that does 2d6+Con Cold and Radiant damage. He uses it on a Chillborn Zombie (resist 10 Cold, vulnerable 5 Radiant). He rolls 7+5 for 12 points of damage, and thus inflicts 17 points of damage on the zombie. The zombie's resistance to cold never comes into play, because the vulnerability overrides it.
The only time you'd get multiple instances of damage would be a power like Prismatic Beams, which specifies that it does 2d6+Int poison, 2d6+Int fire, and dazes.
It is my understanding that the vulnerability to radiant damage doesn't override the resistance to cold, rather it's the lack of resistance to radiant that what makes all the damage go through.
The vulnerability just makes him take more damage when he is hit by radiant damage, unrelated to what resistances the creature may or may not have.
It's possible to be both resistant and vulnerable to the same damage type (such as Resist Cold 10, and then gaining vulnerable cold 5 due to being attacked by someone with the Lasting Frost feat).
In this case, if you get hit by an attack that does 6 cold damge your resistance drops the damage to 0, but your vulnerability causes you to take 5 cold damage anyway (at least that's my current understanding of how it works).