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For cleaning, I'd say it depends on what part of the knife you want to clean, and what you want to clean off.
For cleaning anything metal I use WD40.
For cleaning synthetic materials like G10 or micarta, I use dish detergent, hot water, and maybe some type of plastic bristle brush.
For storage (when I think "storage" I think long term), I don't like coating knives with oils or greases, because those can change over time. They can become thick, sticky, gooey, or even harden into a crust.
Instead, I would use an air-tight container, and maybe add some desiccant packs. That way if I suddenly want to use one of the knives I don't have to clean any oils/coatings off first. Pelican/Storm cases are good, but Harbor Freight sells their own brand of air-tight cases (Apache) which are far less expensive but still good quality (I have one, and wouldn't hesitate to buy more).
I would also store folders with dry pivots for the reasons already given. From my years of working dirty, dusty construction jobs I prefer dry pivots anyway.
And shane45 was right about not storing knives in leather sheaths, because chemicals used to process the leather can be corrosive over time and damage blades, as well as other metal parts like guards, bolsters, handles, etc.
Also, kydex sheaths should not be stored anywhere that they are exposed to high temps, like temps in the 90's or low 100's, because heat can cause them to deform. I've had a kydex sheath loosen up significantly simply from ambient summer heat, and I've seen kydex sheaths ruined as a result of sitting in hot cars, and hot attics.