Don't know about easiest but if cloth is really dirty pull the material and throw in washer. Use Wheel Cleaner or Dawn. Sonetimes soaking overnight in this in a barrel will help.
I know this is a bit late but I think the best way for cleaning brushes is to include them in a scheduled maintenance program. Dirty brushes not only look bad they do not clean was well because they tend not to be as flexible or hold as much water and any lubricating shampoo or detergent. Might be a good idea to keep them clean after you get them clean both for appearances and performance.
Had a foam top brush started to look bad after a couple of years. After much attempts at cleaning it seemed the color was basicaly leaving the mateial leaving grayish black natural??? color behind. Finally replaced it. I would do the same for dirty foam. Let it soak in a barrel of cleaning solution overnight then throw it in a washer. with more of the same.