  We present the results of 3 GHz radio continuum observations of 23
superluminous supernovae (SLSNe) and their host galaxies by using the Karl G.
Jansky Very Large Array conducted 5-21 years after the explosions. The sample
consists of 15 Type I and 8 Type II SLSNe at z < 0.3, providing one of the
largest sample of SLSNe with late-time radio data. We detected radio emission
from one SLSN (PTF10hgi) and 5 hosts with a significance of >5$\sigma$. No time
variability is found in late-time radio light curves of the radio-detected
sources in a timescale of years except for PTF10hgi, whose variability is
reported in a separate study. Comparison of star-formation rates (SFRs) derived
from the 3 GHz flux densities with those derived from SED modeling based on
UV-NIR data shows that four hosts have an excess of radio SFRs, suggesting
obscured star formation. Upper limits for undetected hosts and stacked results
show that the majority of the SLSN hosts do not have a significant obscured
star formation. By using the 3 GHz upper limits, we constrain the parameters
for afterglows arising from interaction between initially off-axis jets and
circumstellar medium (CSM). We found that the models with higher energies
($E_{\rm iso} \gtrsim$ several $\times 10^{53}$ erg) and CSM densities ($n
\gtrsim 0.01$ cm$^{-3}$) are excluded, but lower energies or CSM densities are
not excluded with the current data. We also constrained the models of pulsar
wind nebulae powered by a newly born magnetar for a subsample of SLSNe with
model predictions in the literature.
