Edge-device co-inference refers to deploying well-trained artificial intelligent (AI) models at the network edge under the cooperation of devices and edge servers for providing ambient intelligent services. For enhancing the utilization of limited network resources in edge-device co-inference tasks from a systematic view, we propose a task-oriented scheme of integrated sensing, computation and communication (ISCC) in this work. In this system, all devices sense a target from the same wide view to obtain homogeneous noise-corrupted sensory data, from which the local feature vectors are extracted. All local feature vectors are aggregated at the server using over-the-air computation (AirComp) in a broadband channel with the orthogonal-frequency-division-multiplexing technique for suppressing the sensing and channel noise. The aggregated denoised global feature vector is further input to a server-side AI model for completing the downstream inference task. A novel task-oriented design criterion, called maximum minimum pair-wise discriminant gain, is adopted for classification tasks. It extends the distance of the closest class pair in the feature space, leading to a balanced and enhanced inference accuracy. Under this criterion, a problem of joint sensing power assignment, transmit precoding and receive beamforming is formulated. The challenge lies in three aspects: the coupling between sensing and AirComp, the joint optimization of all feature dimensions' AirComp aggregation over a broadband channel, and the complicated form of the maximum minimum pair-wise discriminant gain. To solve this problem, a task-oriented ISCC scheme with AirComp is proposed. Experiments based on a human motion recognition task are conducted to verify the advantages of the proposed scheme over the existing scheme and a baseline.