The hydrostatic equilibrium and the stability against radial perturbation of charged strange quark stars composed of a charged perfect fluid are studied. For this purpose, it is considered that the perfect fluid follows the MIT bag model equation of state and the radial charge distribution follows a power-law. The hydrostatic equilibrium and the stability of charged strange stars are investigated through the numerical solutions of the Tolman-Oppenheimer-Volkoff equation and the Chandrasekhar's pulsation equation, being these equations modified from their original form to include the electrical charge. In order to appreciably affect the stellar structure, it is found that the total charge should be of order 1020[C], implying an electric field of around 1022[V/m]. We found the electric charge that produces considerable effect on the structure and stability of the object is close to the star's surface. We obtain that for a range of central energy density the stability of the star decreases with the increment of the total charge and for a range of total mass the electric charge helps to grow the stability of the stars under study. We show that the central energy density used to reach the maximum mass value is the same used to determine the zero eigenfrequency of the fundamental mode when the total charge is fixed, thus indicating that the maximum mass point marks the onset of instability. In other words, when fixing the total charge, the conditions dMdρc>0 and dMdρc<0 are necessary and sufficient to determine the stable and unstable equilibrium configurations regions against radial oscillations. We also consider another charge distribution, charge density proportional to the energy density, and show that our results do not depend on this choice and the conditions used to determine regions made of the stable and unstable charged equilibrium configurations are maintained.