Motivated by recent experimental initiatives, such as at the Helmholtz International Beam line for Extreme Fields at the European X-ray Free Electron Laser, we calculate the birefringent scattering of x rays at the combined field of two optical (or near-optical) lasers and compare various scenarios. In order to facilitate an experimental detection of quantum vacuum diffraction and birefringence, special emphasis is placed on scenarios where the difference between the initial and final x-ray photons is maximized. Apart from their polarization, these signal and background photons may differ in propagation direction (corresponding to scattering angles in the millirad regime) and possibly energy.