Sulfur vulcanization is the most common crosslinking technology for unsaturated rubbers. To enhance our generic understanding of the structure–property relationships for sulfur-vulcanized rubber networks, we have studied two low-unsaturated rubbers, IIR and EPDM, and two high-unsaturated rubbers, NR and BR, at varying levels of sulfur curatives. In the first part of this series, the rheometer torque maximum and the compression set as a function of the temperature were discussed. In this second part, the effects of the level of the rubber unsaturation, the density of the trapped entanglements, and the chemical crosslink density on the network structure and tensile properties are discussed quantitatively. Our results reveal that the networks of the vulcanized BR and EPDM consist mainly of trapped entanglements. For EPDM and IIR, all unsaturation can be fully converted to sulfur crosslinks. The tensile strength at break (TS) of vulcanized EPDM and BR is independent of the permanent network density, which is the sum of the chemical crosslink density and the trapped entanglements. The TS shows a pronounced maximum versus the permanent crosslink density for vulcanized IIR and NR, due to the absence of the reinforcing effect of strain-induced crystallization (SIC) at low crosslink densities and the suppression of SIC at high crosslink densities. The elongation at break decreases with increasing network density, following a power-law relation. Mooney–Rivlin analysis of the stress–strain curves confirms our findings of the network structure as obtained from rheometry. However, an unexpected, curved course of the second Mooney–Rivlin parameter as a function of the varying sulfur content is observed for the EPDM samples, indicating that vulcanized EPDM has a different, entanglement-dominated network structure in contrast to IIR, NR, and BR.