In machining, your inhalation hazard is oil mists. Very little will be vapor, and you're not really getting combustion/decomposition products. Mineral oil bases are generally pretty safe when compared to solvents or smoke particulates. Problem with oils is that many have sensitizers added that can cause a stronger response after some period of past exposure than initially. This is why so many people have had issues using Tap Magic. Halfway through the bottle, and the smell makes people feel sick. I would stay to very clean cutting oils. I use castor oil on the lathe because of its high heat tolerance. Otherwise, non-detergent oil or spindle oil works well. It pays to know what's in the products you use, so you can avoid things you are sensitive to. You might react badly to oxygenated hydrocarbons like glycol ethers, esters, or ketones. Stick with plain base oils instead.
If you want to use a respirator for oil mists, you need to get the appropriate P- cartridge for oil Proof. Any kind of ventilation that provides air exchange (as opposed to circulation) is a help, and filtering circulated air is better than not.