Each line adds either one time or zero times. It's a true/false situation.
For example, if you have "+8% Elemental Damage" and you're looking at Lightning Damage that's being converted to Fire Damage, the game will ask "Is this Elemental?," say "yes," then add 8% once.
In contrast, if that node said:
"+8% Fire Damage
+8% Lightning Damage" then it would ask "Is this Fire?" say "yes," then add 8%, then ask "Is this Lightning?" also say yes, and add another 8%.
And a third example: if you have "8% Increased Fire and Lightning Damage", it will ask "Is this Fire or Lightning?", once. If yes, add 8% Increased Damage.
Armour and Evasion passives are an example of this in practice.
All modifiers are applied at the same stage, after Conversion. The Converted damage does benefit from the source-type's damage bonuses.
Thanks Scrotie and Vipermagi, these posts together are probably the best short explaination of this stuff so far, and will be useful to link people to (although I've taken the libery of editing my quote of Scrotie's post to make it clearer that the two bonuses were on separate lines).