I use an ultrasonic every now and again when I pull my reo apart to clean its internals as well.
If you dont have access to an ultrasonic, you can use alcohol. Let it soak in there for a bit to help break up the gunky stuff. Then rinse in hot water.. if you wanna do what I do to help rinse.. I then setup my Odin with no coil on the reo and fill the bottle with clean warm water over the sink and just squirt it thru over the sink.
Everyone may have their own methods but that works well for me.