I prefer to drop an oily, greasy part, like an oil filler cap, into a can of old carb cleaner and letting it "soak" for a week. If your timing is good, you can remove the carb cleaner solvent and most of the crud by rinsing it out in warm, soapy cloths washer water as it's being pumped out of the washer (a deep sink is the preferred location to do this). The actual filter material is usually a form of steel wool which does get cleaner, but not much. Further cleaning steps are solvent based - acetone, kerosene, paint thinner - just to verify the filter material is usable. I have had to toss a few of the oil filler caps because they didn't cooperate in the cleaning process. One cleaner that does not get mentioned is TSP, Tri-Sodium phosphate. I've used TSP mixed with water and the green pyramids in a vibrator cleaner. The pyramids do get stuck in tight corners though.
Have you thought of an ultrasonic cleaner with a little grease lightning or simple green. An untrasonic cleaner is pretty cheap from Harbor freight or ebay and you can use it on many things with cavities and crevices that are hard to reach.
I haven't had that much good results with this type of cleaner. I've used mine on clips and other small parts but was not happy.
Jim