Sulfur-rich polymers (SP) were prepared using styrene as a comonomer in inverse vulcanization with elemental sulfur and used as a vulcanizer for Eucommia ulmoides gum (EUG) modification to generate EUG-SP-x. The effects of SP on the vulcanization process and mechanical properties of EUG-SP-x were investigated. The results showed that the tensile strength and elongation at break increased gradually with the increase of SP from 4 to 8 phr, and EUG-SP-8 displayed a high tensile strength of 29.54 MPa, elongation at break of 573%, and a high toughness of 60.88 MJ m–3, superior to those of conventional vulcanization EUG (EUG-S-5.59 (CB)) and inverse vulcanization NR (NR-SP-8 (CB)). When the amount of SP was 10 phr, the crystallization property of EUG was greatly damaged, and EUG-SP-10 showed the stress–strain curve of elastomers. Dynamic mechanical analysis results showed that tanδ of EUG-SP-8 is 0.3 at −45 °C, 0.111 at 0 °C, and 0.014 at 60 °C, portending excellent low rolling resistance and potential application in green tires. Sound absorption properties and shape memory capabilities were also investigated. EUG-SP-xs displayed improved sound absorption property at room temperature and excellent shape memory capability with quick recovery at moderate temperatures.