A rigorous theoretical investigation has been made on the nonlinear propagation of dust-ion-acoustic shock waves in a multicomponent magnetized pair-ion plasma having inertial warm positive and negative ions, inertialess non-thermal electrons and positrons, and static negatively charged massive dust grains. The Burgers' equation is derived by employing reductive perturbation method. The plasma model supports both positive and negative shock structures in the presence of static negatively charged massive dust grains. It is found that the steepness of both positive and negative shock profiles declines with the increase of ion kinematic viscosity without affecting the height, and the temperature of the electrons enhances the amplitude of the shock profile. It is also observed that the increase in oblique angle rises the height of the positive shock profile, and the height of the positive shock wave increases with the number density of positron. The application of the findings from present investigation are briefly discussed.