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.
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