Number one: run water in the sinks for the P trap may have dried up as it may not have been used in years. A cup of water is all you need. Otherwise you are smelling septic or sewer gases. Fill all drains with a cup of water so you know it is not the sewers(including the floor drain in the basement)
Now, the wood is not rotting. If the cabinets are dry as they usually are to hold dishes, foodstuffs, and spices and sometimes linens they would be dry. The cabinet doors keeps the dust out(especially from forced air furnaces).
Usually under the sink is the cleaning products AND a 2 gallon garbage pail. The other cabinets would hold steel pots and pans. Everything is washed and ready to go and you know where everything is because it is your set up Maybe even canning, potatoes, onions, garlic. old gym socks.
Okay? unfinished surfaces smell are like a bunch of tiny empty pockets (that used to hold tree sap odour which now has been DISPLACED by holding in the odours of the last users of the kitchen as the sap dries up.
. Which means various cooking smells, fire smells, body odour smells that you are not familiar with; all that get sucked in like a sponge molecule by molecule. And it slowly releases as it absorbs a different molecule of odour. That is the musty old smell.
Most common set up of a kitchen for use.
The kitchen was not wiped down (usually a bleach & water combination) is ragged on to all the surfaces(unfinished and finished) and the doors and drawers are left open fully to dry out. Wipe down the walls with the same mixture (maybe a cup of bleach to 3/4 gallon of water)
Odour molecules have an electric charge so they stick to the walls and any other surface easily.
Another way, as I am getting lazy with old age is to get a plant misting bottle from the dollar store. This is the bottle with the large "C" Trigger for pump action, so you can put 2 fingers on it , and it has an adjustable nozzle for the spray type...either fine mist or a straight stream(which is a good wasp killer using a different chemical)
Put into the container "White vinegar" the stuff that looks like water.. Set the tip to fine mist. Now mist inside the cabinets a light spritz say a shot per upper compartment. And mist the door. Leave open and move to next cabinet and do the same thing. Bottom cabinets may take 2 shots as they are larger. Now go to upper cabinets and close the cabinet doors and give it a light misting from about 2 feet away from the door.s Do all the cabinets like this and do the outside of the doors as well. Under the sink where the garbage pail is usually kept hidden you may have to give a triple misting inside - start high and gravity does the rest.. Walls of the kitchen - standing on the floor and about 2 feet away from a corner shoot at a 45 degree angle toward the ceiling. You won,t hit the ceiling with the spray but the odour is in the air and that is what you are trying to remove. White vinegar (bought at any grocery store) does a fine job of not staining and taking the other odours with it when it dries up(maybe half an hour) Works great when you were not watching the stove and something raunchy burns. The vinegar will get rid of that smell in a big way....try burning cabbage black - yeah even the dead turn over in their graves.
Then the smell that remains is basically >>nothing<<
Works too in bathrooms where someone took a smelly dump.