The quality of service (QoS) and quality of experience (QoE) metrics are vital performance indicators in cellular systems. This article presents an analytical study on indoor non-orthogonal multiple access (NOMA) systems empowered by intelligent reflecting surfaces (IRS) in composite $\kappa-\mu$ fading channels. In particular, we consider the network’s QoS through various performance metrics such as outage probability (OP), ergodic capacity (EC), average bit error rate (BER), and system throughput, for which we derive exact and asymptotic closed-form expressions. Furthermore, in contrast to measuring the conventional QoE of a user, we propose to apply the mean score opinion (MOS) factor, in which the objective technical criterion is mutated into a subjective user-recognised quality. To quantify this, a MOS-based QoE evaluation model is applied to an interactive web browsing service. The results demonstrate the impact of IRS on the QoS and QoE of the indoor NOMA users, as well as the effect of manipulating the channel fading components, power allocation coefficients, and path loss factors. It will be shown that careful manipulation of such parameters, coupled with the use of IRS, produce spectacular improvements in system performance. Monte Carlo simulations are performed to corroborate the accuracy of the derived analytical results.