In the present paper, we provide low-frequency dielectric spectra for a thin layer of a nanofluid based on transformer oil and iron oxide nanoparticles stabilized by oleic acid. The complex dielectric permittivity measured in the frequency range from 1 mHz to 200 kHz shows an obvious electrode polarization effect and a Debye-like dielectric relaxation process. Both effects stem from the presence of space charge in the oil due to impurity ions, and in the nanofluid represented predominantly by a residual surfactant and uncompensated particle surface charge. It is shown that the spectra, which were measured in the temperature range from 298 K to 358 K, can be well represented by a fitting function consisted of one Havriliak-Negami term and the Jonscher's power law. In the investigated magnetic nanofluid layer, we found that the onset of the electrode polarization is suppressed to lower frequencies by the application of an external magnetic field (300 mT). This phenomenon is explained by a slowed-down migration of the space charge due to the Lorentz force and by a hindering effect of the formed magnetic nanoparticle aggregates. Surprisingly, a moderate decrease in the whole permittivity spectrum was observed for both parallel and perpendicular orientations of the electric and magnetic fields. This is in contradiction with the usual magnetodielectric anisotropy effect. Based on our qualitative analysis, we discuss potential reasons accountable for the observed effect.