ABSTRACT Mergers of binary neutron stars and black hole-neutron star binaries produce gravitational-wave (GW) emission and outflows with significant kinetic energies. These outflows result in radio emissions through synchrotron radiation. We explore the detectability of these synchrotron-generated radio signals by follow-up observations of GW merger events lacking a detection of electromagnetic counterparts in other wavelengths. We model radio light curves arising from (i) sub-relativistic merger ejecta and (ii) ultra-relativistic jets. The former produce radio remnants on timescales of a few years and the latter produce γ-ray bursts in the direction of the jet and orphan-radio afterglows extending over wider angles on timescales of weeks. Based on the derived light curves, we suggest an optimized survey at 1.4 GHz with five epochs separated by a logarithmic time interval. We estimate the detectability of the radio counterparts of simulated GW-merger events to be detected by advanced LIGO and Virgo by current and future radio facilities. The detectable distances for these GW merger events could be as high as 1 Gpc. Around 20%-60% of the long-lasting radio remnants will be detectable in the case of the moderate kinetic energy of erg and a circum-merger density of or larger, while 5%-20% of the orphan-radio afterglows with kinetic energy of 1048 erg will be detectable. The detection likelihood increases if one focuses on the well-localizable GW events. We discuss the background noise due to radio fluxes of host galaxies and false positives arising from extragalactic radio transients and variable active galactic nuclei, and we show that the quiet radio transient sky is of great advantage when searching for the radio counterparts.