Two years ago I built my wife a 128 sq. ft. cedar closet. I put the clothes rails as far from the walls as possible and bought wooden hangars because essential oils of many kinds will damage plastic. With all that new eastern red cedar planking you could smell the cedar in the stairwell to the second floor. (That stopped when I sealed under the door.) I warned my wife to make sure she stored everything so that it is not in contact with the cedar walls; new cedar sometimes bleeds and you wouldn't want sticky resin on your clothing or purse.
The room is now pretty much airtight. Before filling it I checked the humidity with a certified hygrometer... it was 68%. I ran a dehumidifyer for a few days and lowered the humidity to 55%. There was a puddle of water on the linoleum floor so I disassembled the dehumidifyer and found the styrofoam drip pan was eaten completely through by the cedar oil. Don't store anything with plastic, foam or styrofoam in a cedar closet.
I've checked the humidity in the room twice since then; it was always the same as the rest of the building (50 - 60%). I find it hard to believe that cedar has any effect on humidity. My wife has several dozen purses, shoes and boots stored in the closet. They don't smell when she brings them down from the closet; or they smell fresh.
Cedar oil does not kill moths or their larvre. It might repell them when it is new; it sure smells like it would. It is, however, a great anti-fungal and anti-bacterial. We have cedar posts that I set fifty-five years ago; most are still there. The closet is bug-proof because it is nearly air tight. Without bacterial or fungal growth there is no 'storage' smell on anything removed from the closet.