The imperative advancement of gamma-ray shielding materials is pivotal for ensuring radioactive and nuclear safety. In this study, our objective was to ascertain key gamma ray shielding parameters, including the mass attenuation coefficient (μm), effective atomic number (Zeff), half-value layer (HVL), effective electronic density (Neff), mean free path (MFP), and exposure buildup factor (EBF), for four oxyanion complexes (CaMoO4, PbCrO4, PbMoO4, or CaWO4). These calculations were performed using Phy-X software within the photon interaction range of 0.015-15 MeV. The investigated ternary chromate, tungstate, and molybdate complexes with the molecular formula ABO4, where A = Ca or Pb and B = Mo, Cr, or W, exhibited an exponential decrease in μm with increasing photon energy in the low-energy region. Lead molybdate demonstrated the highest μm followed by PbCrO4, CaWO4, and CaMoO4, correlating with their respective mean atomic numbers and densities. The mean free path values followed the order of PbMoO4, PbCrO4, CaWO4, and CaMoO4, indicating superior shielding properties due to effective medium-photon interactions. The HVL increased with rising photon energy, with the minimum HVL observed in the presence of lead, primarily attributed to the photoelectric effect. Zeff exhibited a decrease with diminishing mean atomic number and density, with PbMoO4 displaying the highest Zeff, signifying superior γ-ray shielding capability. The exposure buildup factor (EBF) highlighted the interference of photons by calcium compared to lead compounds. The controlled parameters at low and high energy exposures were attributed to the anion and cation properties of the ternary ABO4, respectively. Among the evaluated materials, PbMoO4 emerged as the most effective gamma shielding material in the context of nuclear safety.