Vehicle detection and classification have become important tasks for traffic monitoring, transportation management and pavement evaluation. Nowadays there are sensors to detect and classify the vehicles on road. However, on one hand, most sensors rely on direct contact measurement to detect the vehicles, which have to interrupt the traffic. On the other hand, complex road scenes produce much noise to consider when to process the signals. In this paper, a data-driven methodology for the detection and classification of vehicles using strain data is proposed. The sensors are well arranged under the bridge deck without traffic interruption. Next, a cascade pre-processing method is applied for vehicle detection to eliminate in-situ noise. Then, a neural network model is trained to identify the close-range following vehicles and separate them by Non-Maximum Suppression. Finally, a deep convolutional neural network is designed and trained to identify the vehicle types based on the axle group. The methodology was applied in a long-span bridge. Three strain sensors were installed beneath the bridge deck for a week. High robustness and accuracy were obtained by these algorithms. The methodology proposed in this paper is an adaptive and promising method for vehicle detection and classification under complex noise. It would serve as a supplement to current transportation systems and provide reliable data for management and decision-making.