This paper considers multiple unmanned aerial vehicles (UAVs) to assist sensing data transmissions from the ground users (GUs) to a remote base station (BS). Each UAV collects sensing data from the GUs and then forwards the sensing data to the remote BS. The GUs first backscatter their data to the UAVs and then all UAVs forward data to the BS by the nonorthogonal multiple access (NOMA) transmissions. We formulate a multi-stage stochastic optimization problem to minimize the long-term time-averaged age-of-information (AoI) by jointly optimizing the GUs' access control, the UAVs' beamforming, and trajectory planning strategies. To solve this problem, we first model the dynamics of the GUs' AoI statuses by virtual queueing systems, and then propose the AoI-aware sensing scheduling and trajectory optimization (AoI-STO) algorithm. This allows us to transform the multi-stage AoI minimization problem into a series of per-slot control problems by using the Lyapunov optimization framework. In each time slot, the GUs' access control, the UAVs' beamforming, and mobility control strategies are updated by using the block coordinate descent (BCD) method according to the instant GUs' AoI statuses. Simulation results reveal that the proposed AoI-STO algorithm can reduce the overall AoI by more than 50%. The GUs' scheduling fairness is also improved greatly by adapting the GUs' access control compared with typical baseline schemes.