Based on low-energy electron diffraction structural investigations of ordered and disordered phases of O/Ni(111) that show that occupation of both fcc and hcp sites can be forced either by thermal activation or by coverage, the lateral interactions and the binding-energy difference of fcc and hcp sites are redetermined for this system by simulating the phase diagram with Monte Carlo simulations, concentrating on the coverage range between 0.25 and 0.33 ML. From a comparison of the temperature dependence of the occupation probability of fcc and hcp sites in experiment and simulations, the difference in binding energy between fcc and hcp sites is determined to be 46 meV. Using a minimum set of five pairwise lateral interactions, the experimental phase diagram in the investigated coverage range is reproduced in detail. Even the complex diffraction patterns experimentally observed in the domain-wall phase are well reproduced in the simulations. We show in particular that this phase is only stabilized by entropy. Critical properties of the p(2×2) order-disorder transition are discussed briefly.