Four series of new 1,2,4-oxadiazole derived bent-core liquid crystals incorporating one or two cyclohexane rings are synthesized and investigated by optical polarizing microscopy, differential scanning calorimetry (DSC), X-ray diffraction (XRD), electro-optical, and dielectric investigations. All the compounds exhibit wide ranges of nematic phases composed of tilted smectic (SmC-type) cybotactic clusters with strongly tilted aromatic cores (40–57°) and show a distinct peak in the current curves observed under a triangular wave field. Dielectric spectroscopy of aligned samples corroborates the previously proposed polar structure of the cybotactic clusters and the ferroelectric-like polar switching of these nematic phases. Hence, it is shown that this is a general feature of the nematic phases of structurally different 3,5-diphenyl-1,2,4-oxadiazole derivatives. In these uniaxial nematic phases there is appreciable local biaxiality and polar order in the cybotactic clusters. As a second point it is shown that electric field induced fan-like textures, as often observed for the nematic phases of bent-core liquid crystals, do not indicate the formation of a smectic phase, rather they represent special electro-convection patterns due to hydrodynamic instabilities.