Progress in electrical engineering puts a greater demand on the cooling and insulating properties of liquid media, such as transformer oils. To enhance their performance, researchers develop various nanofluids based on transformer oils. In this study, we focus on novel commercial transformer oil and a magnetic nanofluid containing iron oxide nanoparticles. Three key properties are experimentally investigated in this paper. Thermal conductivity was studied by a transient plane source method dependent on the magnetic volume fraction and external magnetic field. It is shown that the classical effective medium theory, such as the Maxwell model, fails to explain the obtained results. We highlight the importance of the magnetic field distribution and the location of the thermal conductivity sensor in the analysis of the anisotropic thermal conductivity. Dielectric permittivity of the magnetic nanofluid, dependent on electric field frequency and magnetic volume fraction, was measured by an LCR meter. The measurements were carried out in thin sample cells yielding unusual magneto-dielectric anisotropy, which was dependent on the magnetic volume fraction. Finally, the viscosity of the studied magnetic fluid was experimentally studied by means of a rheometer with a magneto-rheological device. The measurements proved the magneto-viscous effect, which intensifies with increasing magnetic volume fraction.