It is generally believed that only intermolecular, elastically-effective crosslinks influence elastomer properties. The role of the intramolecular modifications of the polymer chains is marginalized. The aim of our study was the characterization of the structural parameters of cured elastomers, and determination of their influence on the behavior of the polymer network. For this purpose, styrene-butadiene rubbers (SBR), cured with various curatives, such as DCP, TMTD, TBzTD, Vulcuren®, DPG/S8, CBS/S8, MBTS/S8 and ZDT/S8, were investigated. In every series of samples a broad range of crosslink density was obtained, in addition to diverse crosslink structures, as determined by equilibrium swelling and thiol-amine analysis. Differential scanning calorimetry (DSC) and dynamic mechanical analysis (DMA) were used to study the glass transition process, and positron annihilation lifetime spectroscopy (PALS) to investigate the size of the free volumes. For all samples, the values of the glass transition temperature (Tg) increased with a rise in crosslink density. At the same time, the free volume size proportionally decreased. The changes in Tg and free volume size show significant differences between the series crosslinked with various curatives. These variations are explained on the basis of the curatives’ structure effect. Furthermore, basic structure-property relationships are provided. They enable the prediction of the effect of curatives on the structural parameters of the network, and some of the resulting properties. It is proved that the applied techniques—DSC, DMA, and PALS—can serve to provide information about the modifications to the polymer chains. Moreover, on the basis of the obtained results and considering the diversified curatives available nowadays, the usability of “part per hundred rubber” (phr) unit is questioned.