In this paper, we consider intelligent reflecting surface (IRS) in a non-orthogonal multiple access (NOMA)-aided Integrated Sensing and Multicast-Unicast Communication (ISMUC) system, where the multicast signal is used for sensing and communications while the unicast signal is used only for communications. Our goal is to depict whether the IRS improves the performance of NOMA-ISMUC system or not under the imperfect/perfect successive interference cancellation (SIC) scenario. Towards this end, we formulate a non-convex problem to maximize the unicast rate while ensuring the minimum target illumination power and multicast rate. To settle this problem, we employ the Dinkelbach method to transform this original problem into an equivalent one, which is then solved via alternating optimization algorithm and semidefinite relaxation (SDR) with Sequential Rank-One Constraint Relaxation (SROCR). Based on this, an iterative algorithm is devised to obtain a near-optimal solution. Computer simulations verify the quick convergence of the devised iterative algorithm, and provide insightful results. Compared to NOMA-ISMUC without IRS, IRS-aided NOMA-ISMUC achieves a higher rate with perfect SIC but keeps the almost same rate in the case of imperfect SIC.