There are some cleaning fluids especially developed for cleaning carbs, make sure u clean with those they do a great job I found a nice carb cleaning kit at, Advance Auto Parts. Has a gallon can much like a paint can. Cleaner is inside w/ a basket with holes in it. Just disassemble the carb (pay attention to how it comes apart) take digital photos if a camera is available. Take lots of photos in the various take down steps. Really helps in reassembly. You put the part in the basket (isn't there a horror movie with this theme that South Park hyjacked one episode?) and lower it into the can of cleaner. Close the can wait overnight and have a look see. A rebuilding kit MIGHT be available.
Probably a brand new carb would save a lot of time and hassle.