You can't really completely get rid of it, but you can cover it up. Try removing the finish and re-finishing the furniture. That should coat the furniture and help protect it from future damage.
The wood has probably been damp for a very long time so let the wood dry completely for a few days in a very dry room. rub generous amounts of murphy's oil soap on the wood and scrub nice and hard. if it doesn't work you may want to put a stain on the wood to cover it.
spray watered down bleach on and in it. everywhere except the finished areas. you may need to do this more than once. follow it up with orange oil so it dosent dry out. you may need to refinish it if the smell is still there.
I like to use Tea Tree Oil. You can purchase this at a discount store in the herb and vitamin section. Wash the furniture with mild soap first and dry well. Then apply this oil with a soft cloth. Apply polish after smell is gone to replenish the wood.
Wet wood often has a musty odor, so making sure the wood is dry would be the first step. Next if it doesn't have any noticeable mold or mildew you could try using a lemon scented furniture polish to clean it up and get rid of the smell.
Some wood oils are sold in various stores. Also using light stains or furniture polish can help remove or hide bad smells. You could also try mild cleaners on the wood surface.
