The useful ingredient in oven cleaner is usually caustic soda, ie sodium hydroxide. It's normally much cheaper than oven cleaner as well. It will hydrolyse practically anything organic given time, but won't touch stainless or other ferrous metals. Anything based on aluminium, magnesium, or other light reactive metals will disappear extremely fast, though, so be warned!
You could try soaking it in a bucket of warm caustic soda solution for a while. I've used it in the past for similar problems and it works well. It's often used in car workshops for old rusty oily parts, because it eats both the oil and the rust. Digesting oil like that is the basis of making soap, of course.
Another effective method is using an enzyme based clothes washing powder or liquid. Again, oils, grease, etc, will be dissolved pretty effectively, if you leave it in a concentrated solution of it for long enough. I often clean saucepans that have baked on crud with this method, just leave it in overnight and rinse it under the tap.
I'd try this first, then the sodium hydroxide if the first method fails. Make sure to wash it very thoroughly before using it again, though, neither is particularly toxic but they taste absolutely horrible even in trace amounts...
pca