We report on the properties of radio-selected galaxies within 30 very-rich Abell clusters with z \lesssim 0.25 . The radio , optical , and x-ray data for these clusters were presented in Paper I ( Morrison et al . 2002 ) . These radio data sample the ultra-faint ( L _ { 1.4 } \geq 2 \times 10 ^ { 22 } W Hz ^ { -1 } ) radio galaxy population with M _ { \mathrm { R } } \leq -21 using the well-known FIR/radio correlation to link the radio with ongoing star formation within individual cluster galaxies . Spectroscopic redshifts exist for \sim 96 \% of the optical identifications . These radio-selected galaxies reveal the ‘ active ’ galaxy population ( starburst and active galactic nuclei ) within these rich cluster environments that can be identified regardless of their level of dust obscuration . These new radio data provide the largest sample to date of low-luminosity radio galaxies within rich cluster environments allowing an unbiased search for dusty starbursting galaxies . For all clusters in our sample , we are sensitive to star formation rates ( M \geq 5M _ { \sun } ) \gtrsim 5 M _ { \sun } yr ^ { -1 } . We have found that the excess number of low-luminosity ‘ starburst ’ radio-selected galaxies ( SBRG ) found by Owen et al . ( 1999 ) in Abell 2125 is not indicative of other rich clusters in our sample . The average fraction of SBRG is \langle f _ { \mathrm { SBRG } } \rangle = 0.022 \pm 0.003 . The A2125 fraction is f _ { \mathrm { SBRG } } = 0.09 \pm 0.03 which is significantly different from the sample average at a > 99.99 \% confidence level . Both A1278 and A1689 are slightly different from the rest of the sample at \sim 90 \% confidence level . The bimodal structure of both the x-ray brightness distribution and optical adaptively smoothed images of A1278 and A2125 suggests that ongoing cluster-cluster mergers may be enhancing this SBRG population . The A1689 excess low-luminosity ( and high-luminosity ) radio galaxy population may be due to interaction with the ICM . The mid-infrared ISOCAM results for A1689 ’ s radio galaxy population suggests that the radio emission for both low- and high-luminosity radio galaxies is AGN in origin except for one radio galaxy . There is a significant spatial distribution difference between the low and high-luminosity ( HLRG ) radio-selected populations . The SBRG have a core radius of 0.40 \pm 0.08 Mpc which is > 3 \times larger than the HLRG core radius . In addition , 48 \% of the SBRGs have colors that are bluer than a typical Sab galaxy compared to 4 \% for the HLRGs . The average absolute magnitude for the SBRG ’ s is \langle M _ { \mathrm { R } } \rangle = -21.93 \pm 0.05 , while for the HLRG ’ s it is \langle M _ { \mathrm { R } } \rangle = -22.33 \pm 0.07 , indicating that the SBRG are less optically luminous than their HLRG counterparts . The HLRGs seem to be a subclass of the cluster ’ s massive red elliptical population , while the SBRGs have a projected radial distribution more like the blue spiral population . Our results indicate that most of the SBRGs are probably gas-rich disk galaxies undergoing \gtrsim 5 M _ { \sun } yr ^ { -1 } of star-formation .