Robust dexterous grasp synthesis has made substantial progress in generating stable, diverse, and physically plausible hand poses. Yet grasping in real manipulation is rarely task-agnostic: a functional grasp must preserve the action possibility specified by the task, contact the appropriate object region, and remain executable by a high-DoF hand. We study open-vocabulary task-oriented dexterous grasp pose generation, where a robot observes multi-view visual inputs, 3D object geometry, and a free-form language instruction, and must generate a grasp that is both physically feasible and functionally aligned. The central challenge is to establish a generalizable perception-action mapping across open-ended task semantics, functional contact selection, and dexterous hand pose generation. We present O PEN D EX G RASP, a unified data, training, and generative modeling framework. At the data level, we build OpenDexVerse, a dualsource data ecosystem constructed by a C2A Recipe (Coverage-to-Alignment): OpenDex-Scale provides broad open-vocabulary coverage through large-scale optimization-generated grasps with vision-language semantic annotation, while OpenDex-Align supplies high-quality embodied functional alignment through human teleoperation and category-level transfer. At the model level, O PEN D EX G RASP learns a shared semantic-geometric latent space that couples multi-view language-conditioned perception with 3D geometric structure. Affordance prediction and grasp pose generation are treated as complementary supervision views over this latent space, allowing the model to ground functional regions while directly generating task-consistent dexterous grasps. Extensive simulation and realrobot experiments show that O PEN D EX G RASP improves open-vocabulary task generalization, functional-region alignment, physical feasibility, inference efficiency, and real-world execution success.