In medieval times they did not have fancy oils and scotch brite pads. Did they obsessively clean the blade and oil it down everytime someone's finger touched it? Or was rust not even an issue and simply a natural property of the sword? Since we don't have color photographs from that time period we don't know what the actual swords in use looked like, whether they were covered in rust or shiny and polished. What effort, if any, was made to prevent rust?

I assume any man worth his salt would make sure to keep his blade well oiled and sharp to prevent the blade from sticking in his scabbard. Most knights had squires and paiges who would look after their armor and weapons during campaigns, however, most regular men-at-arms would hopefully take the time to learn how to care for their weapons and armor, as it was important to their livelihood.

I don't have any sources to back up my claims, but I'm just using my head here. What man would let his sword rust if he knew he would be using it?

There is evidence that some dark age sword scabbards were lined with sheep hide with wool. Lanolin is a very effective moisture inhibitor, as a matter of fact some people rely on lanolin based products today rather than fancy oils and scotchbrite pads.

They did have a form of polishing tool that we see being used on swords and armor in artwork, it appears to be some kind of leather strop on a handle. Other than that you can look into the various finishes blacksmiths use on wrought iron. I like to cook on cast iron and it occurs to me that there's nothing stopping us from using the same seasoning process on swords or armor as the temperature only needs to reach 350 degrees F, thin coats of some oils are essentially transparent too.