One thing to remember if you routinely oil the blade (as I do) is to allow the blade and edge to air dry thoroughly first. If there is any residual moisture on the edge, then the oil is just sealing that moisture in.

My usual routine (subject to correction and improvement because I am not a veteran):
1. Stroke the blade on both sides with my soapy brush using a light stropping stroke, then wipe it with a wet washcloth under the tap, avoiding the edge.
2. Dry the razor on a dry washcloth, using a light stropping motion for the edge.
3. Give it seven or eight light laps on the leather strop, then set it aside to air dry while I rinse my face.
4. Brush the blade lightly with a Q-tip soaked in rubbing alcohol (negative pressure on the edge!); I mean this to act as a dessicant and to get any invisible soapy residue off. Set it aside to air dry while I splash my face with witch hazel and dress.
5. Rub a little mineral oil on the fleshy part of the edge of my hand, and strop the blade lightly on that. Wipe off the excess from the blade, fold it up and put it away in my bedroom away from the bathroom.

(I'd credit the SRP-ers from whom I learned these routines if I could remember them: you all know who you are.)

This is probably overkill, because I have only two razors and so they don't store away for long. But the air drying happens while I do other stuff, so it's not time consuming, and I want to maintain an edge so that I don't have to return to the hone sooner than necessary. Also, our humid summers were putting black spots on my blades when they weren't well dried and carefully oiled over.