In this paper, an experimental analysis of the quality of electrical insulating oils is performed using a combination of dielectric loss and capacitance measurement tests. The transformer oil corresponds to a fresh oil sample. The paper follows the ASTM D 924-15 standard (standard test method for dissipation factor and relative permittivity of electrical insulating liquids). Effective electrical parameters, including the tan δ of the oil, were obtained in this non-destructive test. Subsequently, a numerical method is proposed to accurately determine the effective electrical resistivity, σ, and effective electrical permittivity, ε, of an insulating mineral oil from the data obtained in the experimental analysis. These two parameters are not obtained in the ASTM standard. We used the cell method and the multi-objective non-dominated sorting in genetic algorithm II (NSGA-II) for this purpose. In this paper, a new numerical tool to accurately obtain the effective electrical parameters of transformer insulating oils is therefore provided for fault detection and diagnosis. The results show improved accuracy compared to the existing analytical equations. In addition, as the experimental data are collected in a high-voltage domain, wireless sensors are used to measure, transmit, and monitor the electrical and thermal quantities.