We use a bond-operator mean-field theory and a generalized spin-wave theory to study the frustrated spin-1/2 dimer Heisenberg model on a square lattice with frustrations in both cardinal and corner directions. We establish the ground state phase diagram with very rich phases. It has been disclosed that the frustrations in cardinal directions can induce exotic superfluid (SF) and supersolid (SS) phases. By introducing the frustrations in corner directions, we found more interesting phases, such as the striped superfluid (S-SF) and the striped supersolid (S-SS). We also investigate the excitation spectra and analyze the anisotropic spin-wave velocities of the stripe phases.