The present investigation discusses the influence of obstacle configurations on the hydrothermal and irreversibility characteristics of a sinusoidal backward-facing step channel. The study investigates the interplay of obstacle configuration, namely profiles, locations, and orientations. Different obstacle profiles of identical areas, including square, rhomboid, triangular, circular, and elliptical, are studied. Nusselt number, pressure drop, irreversibility, and hydrothermal factor are the output parameters. Our results highlight that the reattachment length decreases because of the obstacle placed near the channel's inlet, independent of the obstacle's geometrical configuration. Further, the recirculation zone length is found to be the smallest for the square obstacle. The local Nusselt number is found to be greatest at the location of the obstacle, and the peak value of the local Nusselt number is greatest for the backward-facing step channel with a rhomboid obstacle. It was observed that the average Nusselt number, pressure drop, and irreversibility characteristics all increase with the increase in Richardson number irrespective of the shape of the obstacle, and are greatest in the case of a triangular obstacle. However, the elliptical obstacle has a higher hydrothermal factor, indicating that it has the optimum obstacle geometry. In addition, elliptical obstacles with step obstruction distance along the x and y axis, namely (Lx = 10 and Ly = 2.2), (Lx = 20 and Ly = 2.2), are considered as optimal obstacle locations. The angular orientation of 0° is found to have the maximum hydrothermal factor. These findings demonstrate the interplay of wall-obstacle architecture on hydrothermal and irreversibility performance and highlight their importance as a design feature.