Mike R is correct on getting the stone clean before you do anything else. The stone cuts the metal and when the surface gets loaded-up, the cut will not be even with the result being uneven wear on the face of the stone. The same will happen with any abrasive material which is why just using a cleaning stick as needed will extend the life of coated abrasives like sanding belts by 5-10 times for wood applications. For metal applications the cleaning stick is combined with a lubricant stick to obtain the same results.
I build special cleaning machines for industrial applications, you don't need one to clean sharpening stones but I will suggest the industrial detergent I get for them because it'll work fine in a pot of water, just use a metal rack to keep the stone off the bottom of the pot and always put the stone in water that is at room temperature - two reasons for this is to prevent thermal shock that can break/shatter the stone and to allow the convection current flow of the water to assist in cleaning. Do not allow the water to boil, simmer is fine, around 195°F tops, when the water gets into a boil, the bubbles are air pockets and they will cause cavitation pitting of the stone's surface just the same as happens to pump impellers subjected to cavitation. You have to watch how much heat you put into cast/molded stones so as not to destroy the adhesive bond holding the abrasive together, for these I generally keep the water temp below 175°F.
Diamond hones come in two flavors, the plug type which may or may not be actual diamond as most are plugs of cubic boron nitride (CBN) in a nylon block so as to make a low-cost product that sells for big dollars. I sell a three-piece set of coated CBN (man-made diamond) hones for $10 that has one each 2"x6" hone in 180, 240 & 360 grit that work great for resurfacing flints & stones as well as working hardened steel and sharpening carbide tooling. CBN is CBN no matter what you pay for it and if over-paying makes you feel better, I'll be happy to help you feel better.
I got away from using any kind of oil on stones/hones years ago despite the fact that it was drilled into my head about the need for "oiling the stone" for as long as I can remember. When you're honing by hand, you're not generating any heat so there's no need nor value for sulfurized and chlorinated cutting oil. Oil is a surface film lubricant that defeats the purpose of grinding a piece of iron down on an abrasive stone, abrasive cutting and edge cutting are two completely different animals. Simple detergent & water is the best, I suggest Ivory Liquid because it doesn't promote corrosion and it doesn't have issues with residuals. About a tablespoon mixed into a gallon of lukewarm water, I tried all kinds other brands and generics, Ivory brand is best (same mix will help remove static problems from plastics too). Use liberally on stone/hones and especially on CBN, diamond and ceramic. When you're done, rinse the stone/hone in warm water, if needed a nylon brush will get anything that sticks. If you're like me and you forget about rinsing, nice thing about Ivory is you can just put the stone/hone in warm water for a few minutes and the residuals will loosen and come right off without fuss - trust me, others are not so user-friendly.
Lately there's been quite a bit of chatter about using soluble oils designed for surface grinding applications so I got some samples to try ... in my experience, it made for a nasty slop mess. Splashed Ivory liquid wipes up without a hassle, slopped soluble oil requires washing off with a detergent and if you get it on wood, you've got a permanent oil spot just as nasty as if you slopped with the good ole Rigid dark cutting oil.