<p>Dusty plasmas exhibit a rich variety of nonlinear structures, such as shock waves and solitary waves. In our research, we have delved into the evolution of multidimensional shock waves in nonuniform dusty plasmas consisting of dust grains with nonadiabatic charge fluctuation and varying sizes, electrons and ions described by a kappa distribution. To gain insights into the propagation characteristic of shock waves, the modified Korteweg–de Vries (KdV)–Burgers equation is derived by using the standard reductive perturbation technique. Numerical and theoretical analysis reveals the presence of two distinct types of shock structures within the system: oscillatory shock structures and monotonous shock structures. The findings underscore the significant impact of inhomogeneity, magnetic field, nonadiabatic dust charge fluctuation, dust size, which follows a power law distribution (PLD), and kappa indices on the behavior of shock waves. These parameters play a crucial role in shaping the characteristics and dynamics of the shock waves in dusty plasmas. The investigated results will provide a deeper understanding of the shock waves’ dynamics within such complex plasma environments.</p>