The damage identification of railway bridges poses a formidable challenge given the large variability in the environmental and operational conditions that such structures are subjected to along their lifespan. To address this challenge, this paper proposes a novel damage identification approach exploiting continuously extracted time series of autoregressive (AR) coefficients from strain data with moving train loads as highly sensitive damage features. Through a statistical pattern recognition algorithm involving data clustering and quality control charts, the proposed approach offers a set of sensor-level damage indicators with damage detection, quantification, and localization capabilities. The effectiveness of the developed approach is appraised through two case studies, involving a theoretical simply supported beam and a real-world in-operation railway bridge. The latter corresponds to the Mascarat Viaduct, a 20th century historical steel truss railway bridge that remains active in TRAM line 9 in the province of Alicante, Spain. A detailed 3D finite element model (FEM) of the viaduct was defined and experimentally validated. On this basis, an extensive synthetic dataset was constructed accounting for both environmental and operational conditions, as well as a variety of damage scenarios of increasing severity. Overall, the presented results and discussion evidence the superior performance of strain measurements over acceleration, offering great potential for unsupervised damage detection with full damage identification capabilities (detection, quantification, and localization).