In this paper, we report isothermal-isobaric molecular dynamics simulation results for total and excess properties of 48 equimolar and 24 nonequimolar ternary mixtures consisting of Lennard-Jones fluids in different nonideal conditions. Energy and size parameters of the components differ appreciably, lying in the range (1 less than or equal to epsilon(BB)/epsilon(AA) less than or equal to 1.75, 1 less than or equal to epsilon(CC)/epsilon(AA) less than or equal to 2) and (1 less than or equal to sigma(BB)/sigma(AA) less than or equal to 1.75, 1 less than or equal to sigma(CC)sigma(AA) less than or equal to 2). Unlike energy and size parameters of mixtures are determined using Lorentz-Berthelot combination rule. Mixtures are considered at four different conditions, (kT/epsilon(AA) = 1, P sigma(AA)(3)/epsilon(AA) = 0.5), (kT/epsilon(AA) = 2, P sigma(AA)(3)/epsilon(AA) = 1.2), (kT/epsilon(AA) = 2, P sigma(AA)(3)/epsilon(AA) = 2.5) and (kT/epsilon(AA) = 3, P sigma(AA)(3)/epsilon(AA) = 2.5). The effects of unlike size and energy interaction parameters on total and excess properties of mixtures deviating from the Lorentz-Berthelot combination rule have also been investigated at two different conditions, (kT/epsilon(AA) = 1, P sigma(AA)(3)/epsilon(AA) = 0.5) and (kT/epsilon(AA) = 2, P sigma(AA)(3)/epsilon(AA) = 2.5). These simulation results have been used to test our recently developed first-order perturbation theory and van der Waals one-fluid theory of ternary mixtures. Perturbation theory is based on the hard sphere reference mixture and involves no mixing rules. Van der Waals one-fluid theory is based on an accurate equation of state for the pure fluids. An extensive comparison of theoretical predictions with simulation results show that, in general, perturbation theory is very successful in describing simulation results for (1 less than or equal to epsilon(BB)/epsilon(AA) less than or equal to 1.75, 1 less than or equal to epsilon(CC)/epsilon(AA) less than or equal to 2) and (1 less than or equal to sigma(BB)/sigma(AA) less than or equal to 1.75; 1 less than or equal to sigma(CC)/sigma(AA) less than or equal to 2). On the other hand, van der Waals one-fluid theory is reliable in describing total properties in the range 1 less than or equal to sigma(CC)/sigma(AA) less than or equal to 1.18 and excess properties in the range 1 less than or equal to sigma(CC)/sigma(AA) less than or equal to 1.25, for all the energy parameter ratios considered in this paper.