We present a computational study of 2p core-level X-ray photoemission spectra of transition metal monoxides MO (M=Ni, Co, Mn) and sesquioxides M2O3 (M=V, Cr, Fe) using a theoretical framework based on the local-density approximation (LDA) + dynamical mean-field theory (DMFT). We find a very good description of the fine spectral features, which improves considerably over the conventional cluster model. We analyze the role of the non-local screening and its relationship to the long-range magnetic order and the lattice geometry. Our results reveal the potential of the present method for the analysis and interpretation of the modern high-energy-resolution experiments.I.