With increase in oxidation number of a particular halogen atom, the acidic character of corresponding oxoacid increases.
According to Lowry-Bronsted concept, a strong acid has weak conjugate base and a weak acid has a strong conjugate base. Now, let us consider the stabilities of the conjugate bases ClO4-, ClO3-, ClO2- bases, ClO formed from these acids, HClO, HClO2, HClO3 and HClO4 respectively. These anions are stabilised to greater extent, it has lesser attraction for proton and therefore, will behave as weaker base. Consequently, the corresponding acid will be strongest because weak conjugate base has strong acid and strong conjugate base has weak acid and vice versa