Your best bet is a filter that contains carbon--it will adsorb some portion of the organics you're tasting. Chlorine dioxide treatment can reduce it in some cases--but it probably depends on the specific water and contaminants.

The Katadyn Hiker has carbon in the cartridge, and I'm sure there are others. You could also make your own carbon filter to use in addition to a biological filter. Aquarium filter carbon would work.

Cheers,