Move the furniture outdoors in the sunlight to dry it out. Alternately, open the windows in the area, run fans on their highest settings to increase the air circulation and run a dehumidifier near the affected object(s). Continue until your oak furniture feels completely dry.
Vacuum the entire surface of your oak furniture using a vacuum cleaner hose attachment to remove loose spores.
Dampen a clean rag with a liquid solution containing one part water and one part rubbing alcohol. Wipe the entire surface of the oak vigorously. For tables and chairs, make sure to wipe between any narrow grooves and on the underside of the surface.
Wipe down the surface a second time, using a cloth or rag dampened only with lukewarm water. Wait about 15 minutes before removing the alcohol, and once again make sure to cover the entire surface with your rag. Wipe with a towel to dry the surface moisture, and place the object(s) in the sun or near a dehumidifier to dry completely.
Wipe the surface with chlorine bleach if any musty odor remains. Dilute the chlorine bleach with four parts water, apply conservatively to a clean rag and wipe. Wait 15 to 30 minutes, wipe with a a second damp rag and dry.