If you intend to store it between seasons, gun oil is as good a choice or better than 3-in-1. Remove it from the sheath while storing it, because there are salts and acidic compounds introduced to the leather during the tanning process that promote oxidation.
For sharpening, a thin oil will serve you well. I use honing oil, which is thinner than gun oil, and haven't tried Clay's suggestion of transmission fluid, but I have more than enough of that in the garage and I'll try that next time.
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Gun oil has rust-inhibiting properties that ordinary lubricating oils do not. If your knife is a folder, don't forget to "oil the joint."

Being a Case XX collector, I use their wet stone product, designed for putting on an edge.

Use Outers' for mechanisms and barrel.

For gun oil, I use CLP and variants, the military uses it because of it's multipurpose, it preserves metal surface so I don't see why you can't use it on knives. But me personally, I just put a light coat of petroleum jelly on my blades [my knives are coated and only have the sharpened edge exposed]. In the field you can just use your common chap-stick in place of the petroleum jelly. The light coat will cover and protect the surface from oxidation will in storage or in the sheath [until you start cutting].