The linear viscoelastic behavior of thermoplastic hybrid inorganic-organic polymers synthesized through radical copolymerization of styrene and styryl-based polyhedral oligosilsesquioxane (POSS), R-7(Si8O12) (C6H4CH=CH2), with R = isobutyl (Bu-i), cyclopentyl (Cp), and cyclohexyl Cy), was studied to reveal a significant influence of the vertex group, R. The glass transition temperatures were found to feature a strong and complex POSS vertex group dependence, with Bu-i playing a plasticizer-like role and Cp and Cy enhancing the glass transition. Rheological measurements showed that all of the copolymers with lower weight fractions of POSS (0 6, and 15 wt %) followed the time-temperature superposition (ITS) principle. The rubbery plateau modulus (G(N)(0)) was found to decrease with increasing POSS content and showed a strong dependence on vertex group, with the ordering (BuPOSS)-Bu-i > CpPOSS > CyPOSS, indicating increasing entanglement dilution with POSS size. At low deformation frequencies, a terminal zone was observed for the (BuPOSS)-Bu-i-based copolymers, like pure PS; however, CpPOSS and CyPOSS copolymers lead to low-frequency elasticity for higher POSS contents, Suggesting a weak physical network, with a particular CpPOSS copolymer revealing critical gel behavior. We ascribe the observed rheological data to two distinct effects of POSS incorporation: (i) the effect of POSS grafting on microscopic topology of polymer chains and (ii) intermolecular interaction between POSS and PS chain segments. From Vogel -Tanmman-Fulcher plots of the terminal relaxation time, the apparent activation energy values for each copolymer series were found to monotonically increase with POSS content, indicating that POSS decreases rheological temperature sensitivity, consistent with tTS analysis for free volume thermal expansivity.