The discovery and optimization of high-entropy alloys (HEAs) with exceptional structural and functional properties presents a promising yet challenging frontier in materials science. In this work, we introduce a comprehensive data-driven approach to navigate a huge chemical space in order to identify HEAs with outstanding mechanical and magnetic properties. After curating a database comprising of 1,842,628 density functional theory calculations with the target design space encompassing 45,886 quaternary and 414,771 quinary equimolar HEAs derived from 42 elements, we employ ensemble learning strategies in order to leverage the combined strength of multiple predictive models to enhance the accuracy and reliability of machine learning modelling on the HEA property predictions. This method effectively captures the complex nonlinear relationships between the compositions and properties of HEAs, leading to a superior predictive performance compared to single-model approaches. Furthermore, this work pioneers the use of multi-fidelity and multi-task machine learning for multi-objective Bayesian optimization (BO) to streamline the discovery of HEAs. By integrating the ensemble learning with multi-fidelity, multi-task, and multi-objective BO, it is demonstrated that the most promising compositions with enhanced mechanical (as represented by the bulk modulus) and magnetic (as represented by the magnetization and Curie temperature) can be identified, offering a powerful tool for the accelerated design of HEAs with tailored properties. This comprehensive methodology can be bridged to experimental investigations straightforwardly, thus sets a new benchmark for the data-driven discovery of multifunctional high-entropy material systems.