I've had good luck with just boiling a pot of water and filling the sink with it, dumping it right over the parts. A little Dawn dish detergent added to the hot water helps. Let it soak a while, then before it cools, drain the sink and spray the parts liberally with hot water to rinse everything off. Don't let anything cool or it will solidify that grease again.
If you are going to refinish the parts and want to keep them de-greased, then follow up with some mineral spirits and an old toothbrush while the parts are still warm, to get any persistent stuff in the nooks and crannies. If you aren't going to refinish, use Hoppe's #9 instead of mineral spirits. Or use it after a first scrubbing with mineral spirits. I usually finish off with some Break Free CLP applied with a toothbrush, let that soak a few days, then wipe everything down with shop towels and reassemble.