The present contribution investigates Index Modulation Aided Non-Orthogonal Multiple Access (IM-NOMA) in simultaneously transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS)-assisted networks. In the proposed IM-NOMA scheme, the information for a specific user (IM user) is spatially modulated across STAR-RIS subsurfaces according to a predefined pattern. Then, the IM user detects its signal using an energy-based maximum likelihood (EML) detection method, which technically leverages the energy of the received signals to identify the active subsurface indices. In this context, the performance of the proposed IM-NOMA scheme is quantified over Beaulieu-Xie (BX) fading channels in terms of pairwise error probability (PEP), bit error rate union bound, and achievable rate. The obtained PEP expressions are then used to derive a tight upper bound on the bit error rate (BER), which is subsequently utilized in quantifying the overall system performance in terms of upper bounded BER and the achievable rate. Finally, we validate the derived analytic expressions with respective results from extensive Monte Carlo simulations that provides valuable insights of the theoretical and practical importance on the achievable performance for all users in the system.