You say feces was left in the toilet unflushed for a day or even days... You also say someone saw a fly nearby... My guess - the wiggling things are maggots laid by fly.
When battling parasites your first line of defense should be an impeccably clean environment. You will never get rid of them or you will keep reinfecting yourself and your family if your home is not absolutely clean. There should never be any standing waste in your toilet - ever. First things first -- fix the toilet so that it flushes properly w/o manual manipulation.