Girth galls are the same as basic saddle rubs only at the girth area; normally just behind the elbow. If these are actually girth galls, just as you ar doing, you want to keep the area clean as well as any tack that touches the area. Clean your girth after every ride if regular leather or rinse if washable.
To treat, use an antibiotic ointment or other type wound ointment to help the wound heal. Use a fleece covered girth in the meantime if the horse doesn't seem to be reacting at all to the sore..some do, some don't. If however your horse is reacting with abnormal behavior, pinned ears, unwillingness to work, bucking or short stepping, you need to stop riding until the sores are completely healed.
As for cause, as you said, sweat is a big contributor, however, dirty tack, a too narrow girth, and even a poorly fitted saddle that allows movement of the girth (either forward and back or side to side) can also add to it.
Another issue is that this may not be girth galls but fungus. A gelding I had a ways back was prone to fungus. He got a case right in the girth area that was just about like you described, small lumps/balls on his coat and skin. Despite early treatment the fungus spread and I had to put the horse on steroids to get it to clear and I used a washable girth for a good month after, washing it in between every ride with a mixture of Betadine and fungus shampoo.