Existing Structural Damage Detection (SDD) methods based on Convolutional Neural Networks (CNNs) often face challenges such as limited training samples, difficulties in network training, and damage quantification. To address these issues, this study proposes a multi-stage SDD method using two-dimensional (2D) CNNs. The SDD process is divided into three stages: damage category classification, single-damage detection, and multi-damage detection, with transfer learning incorporated to optimise the 2D CNN training process across various damage cases. Multi-channel raw acceleration signals are used as inputs, with the outputs providing both damage location and severity for effective damage localisation and quantification. The proposed method is validated through 2D numerical truss models and 3D experimental truss models. Results show that the method accurately identifies damage location and severity, achieving over 95% accuracy in noise-free conditions and 70% accuracy under mixed noise levels of '30%+40%'. Additionally, transfer learning reduces training iterations by 67% and cuts training time by 22%. Optimal configurations include using more than three epochs and a three-layer architecture with 8, 16, and 32 kernels, employing a 4 x 150 convolution kernel size. These findings present an efficient, highly accurate, noise-resistant, and low-hardware-demanding method for SDD, offering valuable insights for large-scale structural health monitoring.