From what I've gathered, it's not possible. You can only use the unit attributes for this so you have a limited amount of custom damage types. You can rename the attributes in the text editor.
So if you want a custom damage type called "Fire" which deals double damage against "Ice" targets, do something like this: Pretend that one of the unit attributes are "Ice". Psionic, for example. Change the name of psionic to Ice in the text editor and just remember to change the attribute bonus factor on all fire effects to 2 against psionic/ice.
(For the record, you can't create custom minerals. You can only use the four resources already in game. Minerals, Vespene Gas, Terrazine and Custom Resource)
Sigh, damn google chrome wouldnt let me post this so i re-wrote it.
The damage response i was looking for is in the "Melee/Ranged/Spell/Splash" damage category as this was supposed to be for spells, seeing as i wanted 1 unit to be able to have multiple spells dealing different types of damage. So seeing as the attributes are attached to the unit itself and not the abilities, thats not exactly what i am looking for.
I do have a plan however, to apply/remove a few buff behaviors that i will use as flags determining what type of damage taken. That way i can use 100% data editor to do things like apply increased damage taken from a specific type but just adding a validator that the unit has the "Damage type buff behavior" to increase.
And for the record, MineralZ has 5 types of resources, not sure if thats just emulated to look like a resource or if they found a way to add more. I would love to know that, but it is possible, even if it is just doing it via a dialog image/label and a tooltip and a custom unit type.
Ghan has said he has fixed this. Monovertex please confirm this fix. This was only a problem with people that had signatures in the upper levels like not the special members but the respected members.