If my clothing gives me 18% balance strength and I cast a Spectral blast, will the 18% be used? The blast is a balance spell but when it comes out it's either storm, ice, or fire. Does my 18% balance strength count?
Acttually no, not from your clothing. The boost to damage from clothing will only apply to true Balance spells such as Instect Swarm, Judgement, and Power Nova as a few examples. Spells which activate other classes such as Hydra and Spectral Blast will not be increased. If your clothing increases those schools then it will increase the damage from those spells as well.
Now addressing what tracinjd said. In his example that is correct because it is not an article of clothing but a blade. If you cast Balance Blade before Spectral Blast or Hydra then it will increase the damage of those spells. If you cast Balance Blade and Elemental Blades then cast Spectral Blast or Hydra it will boost the attacks damage even more.
So to recap, clothing only applies bonuses to the school they affect. Blades and traps do the same except in cases of "general" blades and traps such as Feint, Balance Blade, and Hex which will boost any attack regardless of the school.
Master Coleman is correct. Boosts from gear will indeed increase hydra and spectral blast spells because they are indeed balance spells (you can look at the spell card and see the balance symbol). The *damage* that they do is elemental in nature, but the spell itself is balance.
Even though Spectral Blast and Hydra may appear to be elemental spells, they are in fact Balance spells. I have been playing Skullsplitter (death) and using it on him with no hexes, blades, or traps.
The card itself is supposed to give 440 fire, 365 ice, or 550 storm damage. I have 9% attack on my clothes for all classes, thus my fire is boosted to 480, ice to 398, and storm to 600.
If you are fighting an opposite elemental such as alicane swiftarrow and it pops out with the ice then that attack will be boosted even more.