Brake cleaner all the way, try to get the type that comes in a 5 litre can and apply it with a trigger spray as it's more economical than aerosols.
Get a load of cheap paintbrushes and cut the bristles down, according to how much you cut off you can make the bristles more aggressive so they really get into the pockets where the diff balls sit when it's assembled.
Also wear latex gloves to protect your hands
.