This paper aims at optimizing the crashworthiness of empty and foam-filled thin-walled square columns under oblique impact loading, for variations in the load angle, geometry and material parameters of the column. Another focus is to reveal the relative merits of the optimized configurations for both types of columns under such loads. Dynamic finite element analysis (FEA) techniques validated by theoretical solutions and experimental data in the literature are used to simulate the crash responses of such devices subjected to different impact angles. Based on the FEA results, the Kriging metamodels are constructed for the two columns to predict the crashworthiness criteria of specific energy absorption (SEA) and peak crushing force (PCF) under oblique impact loading, which are set as design objectives in the following multiobjective optimization design (MOD) process. The Pareto fronts are identified for the MOD problems of the two types of columns under both single angle impact and the cases involving multiple impact angles, using the multiobjective particle swarm optimization (MOPSO) algorithm. It is found that the optimal designs are generally different under different load angles for either empty or foam-filled column. Results also indicate that more robust designs against oblique impact could be achieved by including multiple load angles in the MOD process. Compared to the empty column, the optimal foam-filled column may have better crashworthiness under pure axial loading, but the optimal empty column has more room to enhance the crashworthiness under oblique impact.