In this paper, the outage performance of uplink intelligent reflecting surface (IRS)-aided non-orthogonal and orthogonal multiple-access (NOMA/OMA) networks is investigated. Specifically, we consider a two-user equipment (UE) NOMA/OMA network, in which both UEs have both direct (UE→base station (BS)) and reflected (UE→IRS→BS) links. All the links between the UEs and the IRS/BS are modeled either as a Rayleigh or a Nakagami-m variate. To characterize these networks’ outage performance, new statistics for the effective channel gains of the IRS-NOMA/OMA’s UEs are derived. Based on that, closed-form expressions for the outage probability (OP) for each UE are derived. Monte Carlo simulations’ results are provided to verify the accuracy of the analytical results.