We present ultrafast x-ray diffraction (UXRD) experiments on different photoexcited oxide superlattices. All data are successfully simulated by dynamical x-ray diffraction calculations based on a microscopic model, that accounts for the linear response of phonons to the excitation laser pulse. Some Bragg reflections display a highly nonlinear strain dependence. The origin of linear and two distinct nonlinear response phenomena is discussed in a conceptually simpler model using the interference of envelope functions that describe the diffraction efficiency of the average constituent nanolayers. The combination of both models facilitates rapid and accurate simulations of UXRD experiments.