Sensing is envisioned as a key network function of the 6G mobile networks. Artificial intelligence (AI)-empowered sensing fuses features of multiple sensing views from devices distributed in edge networks for the edge server to perform accurate inference. This process, known as multi-view pooling, creates a communication bottleneck due to multi-access by many devices. To alleviate this issue, we propose a task-oriented simultaneous access scheme for distributed sensing called Over-the-Air Pooling (AirPooling). The existing Over-the-Air Computing (AirComp) technique can be directly applied to enable Average-AirPooling by exploiting the waveform superposition property of a multi-access channel. However, despite being most popular in practice, the over-the-air maximization, called Max-AirPooling, is not AirComp realizable as AirComp addresses a limited subset of functions. We tackle the challenge by proposing the novel generalized AirPooling framework that can be configured to support both Max- and Average-AirPooling by controlling a configuration parameter. The former is realized by adding to AirComp the designed pre-processing at devices and post-processing at the server. To characterize the end-to-end sensing performance, the theory of classification margin is applied to relate the classification accuracy and the AirPooling error. Furthermore, the analysis reveals an inherent tradeoff of Max-AirPooling between the accuracy of the pooling-function approximation and the effectiveness of noise suppression. Using the tradeoff, we optimize the configuration parameter of Max-AirPooling, yielding a sub-optimal closed-form method of adaptive parametric control. Experimental results obtained on real-world datasets show that AirPooling provides sensing accuracies close to those achievable by the traditional digital air interface but dramatically reduces the communication latency.