What you want is whitewash, and to make it a yearly ritual - usually part of spring cleaning. Whitewash preserves wood, kills insect eggs and germs and helps with odors. Also, you don't need a clean, scrubbed surface, it will grab dirt and flake off, so you can actually just sweep a really grubby wall, slap on some white wash, repeat a few days later and have it look pristine.
So, 3 parts barn/ag/masonry lime (NOT garden lime) and one part salt. Mix with enough water to make it about the consistency of milk. Do it in small batches and stir frequently - it will settle. Slop it on with a course brush.
Please Note: When you first do this, it will look awful. It will look as if a 3 year old spilled milk on the wall, at best. If you are putting it on new wood, you might even be hard-pressed to see it.
Just take a deep breath, have a little faith that I'm not having a joke on you, shut the door and walk away until morning.
In the morning, when it's dry, you will be stunned at the lovely, pristine whiteness of it.
Sometimes, if you are doing it on old plywood, it will dry yellowed. I don't know what's in old plywood that soaks through, but you can layer a few coats on and it will be alright. Coats of more watery whitewash come out better than trying to make it thicker.