Non-orthogonal multiple access (NOMA) significantly improves the connectivity opportunities and enhances the spectrum efficiency (SE) in the fifth generation and beyond (B5G) wireless communications. Meanwhile, emerging B5G services demand of higher SE in the NOMA based wireless communications. However, traditional ground-to-ground (G2G) communications are hard to satisfy these demands, especially for the cellular uplinks. To solve these challenges, this paper proposes a multiple unmanned aerial vehicles (UAVs) aided uplink NOMA method. In detail, multiple hovering UAVs relay data for a part of ground users (GUs) and share the sub-channels with the left GUs that communicate with the base station (BS) directly. Furthermore, this paper proposes a K-means clustering based UAV deployment and location based user pairing scheme to optimize the transceiver association for the multiple UAVs aided NOMA uplinks. Finally, a sum power minimization based resource allocation problem is formulated with the lowest quality of service (QoS) constraints. We solve it with the message-passing algorithm and evaluate the superior performances of the proposed scheduling and paring schemes on SE and energy efficiency (EE). Extensive experiments are conducted to compare the performances of the proposed schemes with those of the single UAV aided NOMA uplinks, G2G based NOMA uplinks, and the proposed multiple UAVs aided uplinks with a random UAV deployment. Simulation results demonstrate that the proposed multiple UAVs deployment and user pairing based NOMA scheme significantly improves the EE and the SE of the cellular uplinks at the cost of only a little relaying power consumption of the UAVs.