Water softeners do not remove most taste and odor problems (although they can remove the metallic taste of iron in water).
1. Odors are typically caused by hydrogen sulfide (“rotten egg smell”) in wells or “bleach” smell in chlorine treated water; both of these causes can be resolved using an activated carbon filter in conjunction with a water softener.
2. The self-sacrificing rod installed in your hot water heater can sometimes be the cause of your odor in the hot water. Having a qualified plumber replace this rod could solve this problem.