To understand the effect of chemical composition, crosslink density, and microstructure on the linear and non-linear viscoelasticity of ethylene propylene diene monomer rubber (EPDM), we carried out high-frequency oscillatory shear molecular dynamics simulations at varying shear strain rates. Sweeping through different EPDM compositions with varying ethylene, propylene and diene ratios, a positive correlation was observed between ratio of propylene monomer and storage modulus of EPDM in the high-frequency glassy regime. For small deformations in this regime, we found that the simplest measure of local molecular stiffness, namely the Debye-Waller factor, is predictive of storage modulus and loss modulus of 20 unique systems with distinct compositions and cross-link densities. Factors that reduce the Debye-Waller factor, such as cross-linking or increased PP content generally result in higher moduli. Remarkably, large-amplitude oscillatory shear simulations revealed that dissipation becomes strongly influenced by polymer entanglements, which results in divergent optimal compositions for small strain vs. large-strain applications of EPDM. We also utilized time-temperature superposition to extrapolate the results from computationally efficient high-strain rate simulations to lower strain rates, demonstrating predictive ability across a wide-range of strain-rates or temperatures. Our findings illustrate some of the important molecular mechanisms underpinning the constitutive behavior of elastomers and pave the way for multi-scale analyses linking composition and microstructure to performance.