We present the star cluster catalogs for 17 dwarf and irregular galaxies in the $HST$ Treasury Program "Legacy ExtraGalactic UV Survey" (LEGUS). Cluster identification and photometry in this subsample are similar to that of the entire LEGUS sample, but special methods were developed to provide robust catalogs with accurate fluxes due to low cluster statistics. The colors and ages are largely consistent for two widely used aperture corrections, but a significant fraction of the clusters are more compact than the average training cluster. However, the ensemble luminosity, mass, and age distributions are consistent suggesting that the systematics between the two methods are less than the random errors. When compared with the clusters from previous dwarf galaxy samples, we find that the LEGUS catalogs are more complete and provide more accurate total fluxes. Combining all clusters into a composite dwarf galaxy, we find that the luminosity and mass functions can be described by a power law with the canonical index of $-2$ independent of age and global SFR binning. The age distribution declines as a power law, with an index of $\approx -0.80\pm 0.15$, independent of cluster mass and global SFR binning. This decline of clusters is dominated by cluster disruption since the combined star formation histories and integrated-light SFRs are both approximately constant over the last few hundred Myr. Finally, we find little evidence for an upper-mass cutoff () in the composite cluster mass function, and can rule out a truncation mass below $\approx 104.5$M$\mathrm{<mrow\; data-mjx-texclass="ORD">\odot </mrow>}$ but cannot rule out the existence of a truncation at higher masses.