I think it's easiest to consider multiple damage types from a single attack as separate and independent of each other. Anything that reduces or enhances one type of damage does not affect the other.
As Destil said, special effects are negated when the primary damage is negated by DR. Examples of things that are negated are: poison, bleeding from a wounding weapon, sleep arrows, arrows of slaying, beheading from a vorpal weapon, and so on. In order for these effects to occur, at least 1 point of damage needs to get through the DR. (It doesn't matter whether it is 1 point or 101 points, as long as something gets through.)
But this does not apply to bonus energy damage (cold, fire, lightning, acid, sonic) from magical weapons, which always bypass DR.
For example, take the case of a hit from a frost, shock, screaming, vorpal long sword +1 against the salamander.
The a hit would do this damage:
1d8 (physical) + 2d6 (cold) + 1d6 (lightning) + 1d6 (sonic)
Physical damage is subject to DR, so it is possible that the salamander could soak all the physical damage with its DR. If all the physical damage is prevented by the DR, the vorpal effect (beheading) is also negated. Whether all the physical damage is negated or not, the salamander still takes the energy damage, which is: 2d6 (cold) + 1d6 (lightning) + 1d6 (sonic).
Since a salamander is of the fire subtype, the cold damage (normally 1d6) is doubled to 2d6. This damage ignores DR.
The lightning and sonic damage (1d6 each) are applied normally, and they both ignore DR.
