We present VAPOR, a novel method for autonomous legged robot navigation in unstructured, densely vegetated outdoor environments using offline Reinforcement Learning (RL). Our method trains a novel RL policy using an actor-critic network and arbitrary data collected in real outdoor vegetation. Our policy uses height and intensity-based cost maps derived from 3D LiDAR point clouds, a goal cost map, and processed proprioception data as state inputs, and learns the physical and geometric properties of the surrounding obstacles such as height, density, and solidity/stiffness. The fully-trained policy's critic network is then used to evaluate the quality of dynamically feasible velocities generated from a novel context-aware planner. Our planner adapts the robot's velocity space based on the presence of entrapment inducing vegetation, and narrow passages in dense environments. We demonstrate our method's capabilities on a Spot robot in complex real-world outdoor scenes, including dense vegetation. We observe that VAPOR's actions improve success rates by up to 40%, decrease the average current consumption by up to 2.9%, and decrease the normalized trajectory length by up to 11.2% compared to existing end-to-end offline RL and other outdoor navigation methods.