Here is what I have tried so far: laundry detergent, pre-wash spray, rubbing in cornstarch, and dishwashing liquid. This is just a regular oily splotch, not axle grease or anything like that.
Just checking - has the item in question gone through the dryer yet? If so, you’re out of luck.
Tried Carbona Stain Devil? Oxy-Clean (or a generic equivalent)?
Hmm, my go-to is dishwashing liquid, and if that didn’t do it (wetting the clothes, rubbing the liquid right into the spot, then washing in hot water), I’m out. Like Ferret Herder says, if you’ve set the stain in the dryer, you might have to just keep on working on it for a couple more washes and see if you get anywhere.
I’ve never tried it, but Heloise says artificial sweetener works.
I’ve had good luck with carpet cleaner. Test an inconspicuous spot first though.
I’ve had oily stains (food related) require repeated dishwashing liquid treatments to come out. 9 times out of 10, it’ll come out on the first try, but not always.
Also, some brands of dishwashing liquid seem to work better than others. The basic varieties of Ajax and Dawn are pretty solid. Anything that’s “soft on your hands” is to be avoided for laundry purposes.
I’ve had great luck with rubbing some baby powder into the grease spot. Let it sit a day or two, then wash. It’s worked for me, so far.
The waterless hand cleaner Go-Jo that is commonly used on mechanic’s hands works great on grease stained clothes. Rub it into the spot and let it sit for a few minutes and re-wash in the machine. We keep some in the laundry cabinet along with the other detergents. Stop by the auto parts store and pick some up.
I’ve had very good results with Dawn. My husband likes to tinker on engines, and so this happens now and then.
The stain I have is just some kind of oil stain. There’s no dirt or grime or anything. It might be cooking oil or something similar.
I second the Go-Jo. It’s awesome on all kinds of greasy stains and adhesives. Make sure to check the item before drying it in the dryer- if the stain’s still there, air-dry and repeat.
If Dawn doesn’t get it out, about the only other option is dry cleaning fluid or naptha. Naptha is easy to find at the paint store, but it’s inflammable and if you’re not careful, you can wind up turning a small oily spot into a saucer-sized halo.
The last time I used it, I did it outside, using enough naptha to flood the stained area, then immediately dunked it into a bucket of soapy water (with Dawn) to get the naptha out. Hand-washed it, then rinsed and let to air-dry. Once I was satisfied the stain was gone, the shirt went into the regular laundry.
Scissors. 
Put a liberal quantity of ammonia on it. Best is to roll it up so that the stain is facing out, then plop it stain down in a shallow bowl of ammonia. Do not then use bleach on this item!
Ammonia works well on oily stains, and on things like sweaty clothes.
Back when I worked production in a food processing plant, some stuff called Lestoil was my go-to grease fighter. I liberally spotted the stain and left it for an hour or so before washing.
Right, that’s what I was going to say. Works very well on grease & oils stains- before they are set in.
Dawn is the one I use, too. It does work best when you catch the stain when it’s fresh, but I’ve used it successfully on stains that I didn’t see until after I’d washed them.
I agree with Dawn–just make sure you don’t put the soiled item in the dryer. Then you’re pretty much screwed.
acetone
I’d Shout it out.