Nanofluids (NFs) with their superior electrical and thermal properties are promising alternate liquid dielectric in power transformers. Alongside the electric field, the magnetic field is also an integral part of power transformers. It accounts for power transfer through flux linkages and due to the design constraints, flux leakages exist in every transformer. This leakage flux interacts with the liquid insulation incessantly. This article aims at studying the magnetic response of the conductive, semi-conductive, and insulating nanoparticles (NPs) and their NFs prepared using mineral oil (MO) and vegetable oil (VO) as the base liquids. Quasi-static and dynamic magnetic fields are applied to the NPs and their NFs to magnetically characterize them by using a vibrating sample magnetometer (VSM) and an electron spin resonance (ESR) spectrometer. Magnetic susceptibility and resonance field are obtained from the magnetic response studies.