The microphase-separated structures of block copolymers have been widely studied to understand the complex mechanism and the comprehensive framework of the microphase separation of the copolymers, which depended primarily upon the copolymer composition, the molecular weight, and temperature. In this work, the morphology and the mechanical properties of a SIS triblock copolymer with 18.3 wt % of polystyrene (Vector 4111) were investigated. Vector 4111 was structurally quite unique in the sense that it possessed two order-order transitions at different temperatures and an order-disorder transition at high temperature. The different microstructures in the different phases of Vector 4111 were obtained by annealing at different temperatures, confirmed by AFM and SAXS: the hexagonally aligned cylindrical phase was obtained when annealed below 185 degrees C, the spherical phase adopting a body-centered cubic (BCC) arrangement was formed at 185 degrees C < T < 215 degrees C, the misaligned spherical phase was obtained at 215 degrees C < T < 280 C, and finally the completely disordered phase was obtained above 280 degrees C. The mechanical testing of Vector 4111 in the different phases was conducted by measuring the stress-strain behavior, the fracture points, the elastic recovery rates, and the elastic modulus followed by the evaluation of the time-temperature superposition. From the results of the stress-strain measurements, it was found that both elastic modulus and fracture stress of the sample in the cylindrical phase were highest, getting lower in the order of BCC spherical, misaligned spherical, and disordered phases, examined by a universal testing machine. It was also found that the time-temperature superposition was valid only within the same microphase-separated region or within the disordered phase. This study would provide an overall picture regarding the relationship between the microstructures and the mechanical properties, including the nonlinear mechanical properties, of a triblock copolymer possessing order-order transitions (OOT) and an order-disorder transition (ODT).