  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 produces radio remnants on timescales of a few years and the
latter produces $\gamma$-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.
$20$--$60\%$ of the long-lasting radio remnants will be detectable in the case
of the moderate kinetic energy of $3\cdot 10^{50}$ erg and a circum-merger
density of $0.1 {\rm cm^{-3}}$ or larger, while $5$--$20\%$ of the orphan radio
afterglows with kinetic energy of $10^{48}$ 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.
