In this study, numerical calculations are employed to investigate the effect of swirl and spiral flow on enhanced heat transfer and pressure drop in internal transversal and helical corrugated tubes with Reynolds numbers in the range of 10,020–40,060 at a constant wall temperature condition. Additionally, a double-objective optimization is employed to obtain the optimal solutions that balance the improvement of heat transfer and flow resistance and relevant design parameters. The results indicate that two reasons exist for heat transfer enhancement. The first reason corresponds to the transformation of convective heat transfer into a jet impingement heat transfer form at corrugation windward. The second reason corresponds to the severely turbulent pulsation and boundary-layer re-development at the corrugation leeside. The spiral flow exerts a low inhibiting effect on the heat transfer performance and causes a significant reduction in the pressure drop. Additionally, the Pareto front is obtained by the genetic algorithm, and equilibrium points with respect to the optimization values of Nu and fRe correspond to 154.6 and 1663.8, respectively, and the design parameters corresponded to Re = 39,596, Hl/D = 0.024, and pl/D = 1.38. Thus, decision-making is performed based on the weight requirement of heat transfer and pressure drop. Optimal solutions are selected from points C–E if heat transfer performance is dominant, and otherwise they are selected from points A–C.