Lattice dynamics and molecular dynamics studies of the oxides UO2 and Li2O in their normal as well as superionic phase are reported. Lattice dynamics calculations have been carried out using a shell model in the quasiharmonic approximation. The calculated elastic constants, phonon frequencies and specific heat are in good agreement with reported experimental data, which help validate the interatomic potentials required for undertaking molecular dynamics simulations. The calculated free energies reveal high pressure fluorite to cottunite phase transitions at 70 GPa for UO2 and anti-fluorite to anti-cotunnite phase transformation at 25 GPa for Li2O, in agreement with reported experiments. Molecular dynamics studies shed important insights into the mechanisms of diffusion and superionic behavior at high temperatures. The calculated superionic transition temperature of Li2O is 1000 K, while that of UO2 is 2300 K.