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The 1,2,4-oxadiazole scaffold has attracted considerable interest as a privileged structure for anticancer drug development due to its favorable physicochemical properties and multimodal bioactivity. This study presents a comprehensive computational investigation to evaluate the potential of a series of 1,2,4-oxadiazole derivatives as dual inhibitors of the human epidermal growth factor receptor 2 (HER2) and estrogen receptor alpha (ERα), two key drivers in these malignancies. An integrated in silico strategy was employed, combining density functional theory (DFT), molecular docking and dynamics simulations, pharmacokinetic profiling, and machine learning models. Our workflow identified several lead compounds exhibiting promising dual-binding characteristics. Key derivatives demonstrated superior predicted binding affinity and complex stability compared to the reference inhibitor erlotinib. Pharmacokinetic evaluations indicated that the series possesses favorable drug-likeness, with high predicted oral bioavailability and a low risk of cardiotoxicity. Furthermore, machine and deep learning models achieved robust performance in classifying compound activity, underscoring their utility in virtual screening. Collectively, this work validates the 1,2,4-oxadiazole core as a promising scaffold for dual HER2/ERα inhibition and provides a rational, multi-faceted computational blueprint. The identified lead compounds warrant subsequent experimental validation, and the established framework serves as a valuable template for accelerating the discovery of next-generation targeted cancer therapies.