Things that I've heard can be used: mineral oil, vegetable oil, 3-in-1 oil, ATF, kerosene.
Yes these can all be used. ATF should be avoided as it can contain ingredients you don't want on your skin, and there are many reliably safe alternatives.
Commercial honing oils are nine times out of ten just mineral oil (UK: paraffin oil or liquid paraffin), sometimes merely with a colourant added so that it's not quite so obvious that it's only mineral oil. All simple lubricating oils are based on a form of mineral oil (including 3-In-One), and so is baby oil.
If you don't mind the sickly-sweet smell of baby oil that's a perfectly good alternative and many woodworkers use it. Video here from Graham Haydon showing him using baby oil on his India stone.
You can of course avoid the smell and just use straight mineral oil, but mineral oil alone can be a little heavy on some stones. As a rough guide the finer the stone the lighter the oil you want to use.
In place of kerosene you can use mineral spirits (UK: white spirit), which actually is a very very thin oil. On very fine, dense oilstones spirit works surprisingly well by itself, but is a little too light on many coarser stones, and as mentioned straight mineral oil can be a little too heavy. However a blend of the two can be made to hit the exact viscosity mark you're personally fond of or which best suits the stones you're using.
A great many vegetable oils can used successfully as honing oil. Most pose no problem at all (see note below on rancidity) but you do have to be careful not to accidentally choose a drying or semi-drying oil — which includes tung oil, flaxseed oil, walnut oil, poppy oil, safflower and some forms of sunflower oil. These can start to 'dry' and begin to gel, clogging the stone and making it nearly useless.
Older books often warn of the danger of using linseed oil (a drying oil) on your honing stones for this very reason. Note that flaxseed oil is linseed oil by another name.
Safe oils to use: corn oil, soya oil, most forms of rapeseed oil (canola) and peanut oil. You can also use almond oil, macadamia nut oil and olive oil, but given their higher price they're hardly a practical consideration.
Note: there's no need to worry about vegetable oil going rancid unless you're in the habit of completely flooding the stone and not wiping it down afterwards. Even at that the only real issue is a slightly stale or "off" smell, there's no other negative effect.