Unless you use a solvent that attacks carbon or copper fouling, most solutions will only degrease the parts.
If you use a bore solvent like Hoppe's #9 it will remove copper fouling and at least some carbon fouling.
To remove both carbon and copper fouling, as well as degreasing, you can use something like Slip 2000 Carbon Cutter or an automotive version of it.
It removes carbon fouling by simply soaking for 15 minutes, so I'm not sure what advantage an ultrasonic unit will be.
For standard cleaning you can use a water-based cleaner like Greased Lightning or Simply Green but READ THE LABEL. Simply Green attacks and seriously damages aluminum, and some cleaners can attack finishes.
Ordinary cheap paint thinner is a good degreaser, but it is flammable so you have to watch sparks.
You can also buy commercial cleaning and rinsing solutions from manufactures of ultrasonic units like L&R, but these are expensive.
When using an ultrasonic unit, remember that it removes ALL lubricant, even from tiny holes or crevices no other cleaning method will reach.
You have to be very careful about getting a coat of lube into all areas to protect from rust.