Yes they can kill parasites. They reason why salt works is that it literally implodes pathogens, the salt penetrates into the cell by way of osmosis in which water is drawn into the cell and the organism dies by drowning. I have read Ayurvedic texts about salt water.
You should be using Liver Cleansing products such as Planetary Formulas Bupleurnum blend and can add other products such as methylating products and liposomal glutathione (Readisorb). I have read that people have expelled flukes using Miracle-Mineral-Supplement .