how do salt react with oil to clean the oil-stain from our dish?

Answer 1

i've never heard of salt cleaning oil stains, and as far as i know it cant, salt won't react with oil, because oil is non polar and salt is polar, you need a polar liquid to dissolve a polar substance and vice versa,
now i can tell you how soap or dishwashing liquid cleans oil stains, basically the molecules in soap have 2 ends, one end is polar and the other is non polar, so the non polar end binds to the oil, while the polar end binds to the water and washes it away

hope that helps

Answer 2

It could only be acting as an abrasive.