The answer to oil, water, or dry depends on who you ask. SharpeningSupplies.com did some testing and they generally state, do not sharpen dry:
https://www.sharpeningsupplies.com/Shou ... -W115.aspx
There is talk about build-up and similar.
Norton India and Crystolon stones. Norton states the following: “Water is less messy, but we recommend using oil as it is more effective than water at keeping the stones from loading.” Also note that “most Norton benchstones are impregnated with oil as part of our manufacturing process.”
Diamond Stones. Sharpening supplies recommends water because there are no pores to fill on diamond plate. If I use water, I always add just a drop or two of Dawn dish washing detergent. I have had rust on my diamond plates when I use water.
The the DMT FAQ states: While we recommend you use DMT® products dry or with water only, it is acceptable to use a variety of lubricants when sharpening with DMT® products. Mineral oil, mineral spirits, kerosene, WD40 can all be used without harming your DMT®.
Best Sharpening Stones recommends Krud Kutter because it works well and is very inexpensive. Obviously Trend recommends their fluid claiming that WD40 (and similar) are too thick causing skating. And their product reduces rust. I find it too expensive.
I often use Smith’s, a non-petroleum based and features built-in stone cleaning agents and rust/corrosion inhibitors. Very happy with it. It has worked fine for me on Arkansas stones as well.
Gatco honing oil also claims usability with Diamond plates, but also with their other sharpening stones. Their Ultimate Diamond Hone Sharpening System includes this oil; well, I think that all of their sharpening systems come with and recommend this oil. It has worked fine for me on Arkansas stones as well.
Shapton Glass Stones. I like them because I do not like soaking. The Shapton FAQ says that although you can use oil, once you use oil you should always use oil. I only use water here.
Water Stones. Water stones, especially those that you soak, I have only used water. I prefer Shapton stones that I do not have to soak, however.
Ceramic stones such as Norton Ascent and Spyderco all claim that they can be used dry. I find that they load less if I spritz them with water. Note that the Spyderco Medium stone (brown) absorbs a lot of water when you do this. I do not always do this, for example, when chip carving or when using my Spyderco Sharpmaker.
Arkansas Stones. I never use these dry and I have only ever used a light oil. The claim is that a light mineral oil prevents clogging better than water. Some testing done by people in the Badger and Blade forum tested with Water, Smith’s honing solution (water soluble version), and a light oil found that with water and with Smith’s the stone would eventually glaze (develop a highly reflective surface from a non-reflective matte surface). A claim is also made that the stone will cut faster and longer when using a light oil. From what I can tell, the coarser the stone, the more likely it will work OK with water, but the pores will still fill faster than with oil. So I do not use water with Arkansas stones.