The acidic strength of an oxoacid depends on the oxidation state of the central atom. A higher oxidation state increases the electron-withdrawing nature of the central atom, which in turn weakens the O-H bond and makes it easier to release an $H^+$ ion. The oxidation states of the central atoms in the given compounds are: Cl in $HClO_3$ is +5, Cl in $HClO_4$ is +7, S in $H_2SO_3$ is +4, and S in $H_2SO_4$ is +6. Since chlorine in $HClO_4$ has the highest oxidation state (+7), it is the strongest acid among the given options.