It is predicted theoretically that various oxides (Al2O3, MgO, SiO2 and TiO2) under ultrafast excitation of the electronic system exhibit nonthermal phase transitions. In the bulk, Al2O3 transiently forms a superionic phase via nonthermal phase transition, MgO and SiO2 disorder, TiO2 experiences solid-solid phase transition while thermal effects lead to melting. In the finite-size samples and near-surface regions, MgO undergoes solid-solid phase transition at lower doses than those required for atomic disorder. All studied oxides but TiO2, if allowed to expand, exhibit a lower damage threshold, whereas in TiO2 expansion releases the stress and prevents solid-solid phase transition thereby increasing the damage threshold up to the melting one. The results suggest that a nonthermal phase transition is a general response of oxides to sufficiently high ultrafast electronic excitation. A comparison with nonadiabatic simulations demonstrates that Born-Oppenheimer approximation systematically overestimates damage thresholds, and in some cases misses a phase transition entirely.