Entropy stabilized oxide of MgNiCoCuZnO5, also known as J14, is a material of active research interest due to a high degree of lattice distortion and tunability. Lattice distortion in J14 plays a crucial role in understanding the elastic constants and lattice thermal conductivity within the single-phase crystal. In this work, a neuroevolution machine learning potential (NEP) is developed for J14, and its accuracy has been compared to density functional theory calculations. The training errors for energy, force, and virial are 5.60 meV/atom, 97.90 meV/Å, and 45.67 meV/atom, respectively. Employing NEP potential, lattice distortion, and elastic constants is studied up to 900 K. In agreement with experimental findings, this study shows that the average lattice distortion of oxygen atoms is relatively higher than that of all transition metals in entropy-stabilized oxide. The observed distortion saturation in the J14 arises from the competing effects of minimum site distortion, which increases with increasing temperature due to enhanced thermal vibrations, and maximum site distortion, which decreases with increasing temperature. Furthermore, a series of molecular dynamics simulations up to 900 K are performed to study the stress–strain behavior. The elastic constants, bulk modulus, and ultimate tensile strength obtained from these simulations indicate a linear decrease in these properties with temperature, as J14 becomes softer owing to thermal effects. Finally, to gain some insight into thermal transport in these materials, with the so-developed NEP potential, and using non-equilibrium molecular dynamics simulations, we study the lattice thermal conductivity (κ) of the ternary compound MgNiO2 as a function of temperature. It is found that κ decreases from 4.25 W m−1 K−1 at room temperature to 3.5 W m−1 K−1 at 900 K. This suppression is attributed to the stronger scattering of low-frequency modes at higher temperatures.