The measurements of residual dipolar couplings in elastomer system is desirable, because they reflect the hindrance to molecular motions by the cross-linking, topological constraints and the external factors like mechanical stress. Dipolar-encoded longitudinal magnetization nuclear magnetic resonance (NMR) decay curves, double-quantum and triple-quantum NMR buildup intensities for measuring the residual dipolar couplings, and the associated dynamic order parameters are introduced. It is shown that in the short excitation time regime the effective dipolar network is simplified. In the limit of this model based on localized dipolar couplings, the spin response to two-dimensional pulse sequences used to record multiple-quantum (MQ) NMR coherences was evaluated for longitudinal magnetization, double-, and triple-quantum coherences of methylene, and methyl protons in synthetic 1,4-cis-polyisoprene. The dynamic order parameters can be evaluated from this NMR response using a classical scale-invariant polymer model. These dynamic order parameters were measured for a cross-link series of synthetic polyisoprene and correlated with the cross-link density. The decay rates of the Hahn-echo amplitudes reflecting residual dipolar couplings as well as effects of molecular motion are also measured for the same cross-link series. The contribution of molecular motions to the transverse relaxation can be separated from the residual dipolar couplings using a train of magic echoes. The sensitivity of these transverse relaxation rates to the cross-link density is compared to that of residual dipolar couplings. The NMR time scale is shorter for the dipolar-encoded longitudinal magnetization and MQ experiments as compared to transverse relaxation experiments leading to an increased sensitivity to cross-link density of the former approaches.