This paper considers an uplink wireless powered multichannel internet of things (MC-IoT) system with multiple hybrid relays, each serves a group of wireless-powered IoTDs. For coordinating radio frequency wireless power transfer (RF-WPT) and wireless information transfer (WIT), two cooperative protocols integrating non-orthogonal multiple access (NOMA) and orthogonal multiple access (OMA), namely hybrid NOMA-frequency division multiple access (FDMA) and hybrid NOMA-time division multiple access (TDMA), is proposed. For both protocols, we investigate cooperative resource allocation problems and aim to maximize the sum data delivered by all the IoTDs, subject to the peak transmit power constraint and the total consumable energy constraint of the hybrid relays. The problem with the hybrid NOMA-FDMA is first decomposed into two subproblems, one for time and power allocation of each hybrid relay and its associated IoTDs, and the other one for channel allocation among them. After some properties of the optimal solution are discovered and a series of transformations is performed, the former subproblem is solved by the bisection search and the Lagrange duality method, and the latter subproblem is solved by the Kuhn–Munkres algorithm. The problem with the hybrid NOMA-TDMA is first convexified by proper variable transformations and then solved by the Lagrange duality method. We provide extensive simulations to demonstrate the superiority of the proposed schemes. It is shown that various system parameters play key roles in the performance comparison of the two schemes.