Answer
An acid that breaks down completely and gives off many ions, or protons, is considered to be a strong acid. ex H₂SO₄
If you place strong acid into water it dissociate acid into H⁺ ions
Water is polar solvent(H⁺ and OH⁻), which has partial positive charge on one side and partial negative charge on the other side.
Strong acids readily dissociate in polar solvents to give H+ ions.
Where as Oil is a non polar solvent it has same charge all over so no dissociation of strong acid will take place.