If the root is already soft or completely black, that part is dead and you need to cut it off without hesitation. Use scissors or a knife disinfected with alcohol or diluted bleach, and don't be afraid to be aggressive: it's better to lose a piece of healthy root than to let the fungus spread.
After cutting, what really works is changing all the substrate. People tend to think that just letting it dry is enough, but the moss or bark where the pot was living is still full of spores. Take the orchid out, get rid of all the old soil, dry the roots well with paper towels (without rubbing), and repot it in fresh, clean substrate. While you're doing this, check that there are no black spots left on the roots you want to keep; if you're in doubt, it's better to cut.
Once planted, don't water for a few days. After that, water but be really careful with standing water: if you use a pot with drainage holes and put it on a tray, take the orchid off it after a few minutes. The fungus needs that humid, waterlogged environment to thrive, so the best thing is not to leave it on the water tray again. The odd smell should disappear in a couple of weeks if the plant starts to recover.