Rheo-optical studies were conducted on a polystyrene-block-poly(ethylene-alt-propylene) copolymer having spherical microdomains composed of polystyrene block chains in a matrix composed of poly(ethylene-alt-propylene) block chains. Small-angle X-ray scattering (SAXS) was detected with a 2D detector simultaneously with stress measurements on specimens subjected to a large-amplitude oscillatory shear deformation with a strain amplitude of 50% and a zero static strain at a frequency of 0.0936 rad/s and at room temperature, with the purpose to elucidate a relationship between macroscopic properties of the systems and their mesoscopic structure as revealed by SAXS. The results indicated that the spheres are packed in a body-centered-cubic (bcc) lattice with a large paracrystal distortion and that the shear deformation induces a preferential orientation of (110) lattice planes parallel to the Oxy plane and the elastic deformation of the bcc lattice under this particular (110) lattice plane orientation. Here Oy is parallel to the direction of the shear displacement vector and Oyz is the plane in which the shear strain exists. The stress amplitude sigma(N) is found to decay with N, the number of strain cycle, and the stress decay to be recovered after cessation of shear. The stress decay with N and the stress recovery after the cessation appear to be interrelated to the preferential orientation of the (110) plane with N and its orientation relaxation after the cessation, respectively. The change of the elastic strain amplitude on the lattice with N and with time after cessation of shear was also proposed to be responsible for the stress decay and stress recovery.