We present a novel system, AdVENTR for autonomous robot navigation in unstructured outdoor environments that consist of uneven and vegetated terrains. Our approach is general and can enable both wheeled and legged robots to handle outdoor terrain complexity including unevenness, surface properties like poor traction, granularity, obstacle stiffness, etc. We use data from sensors including RGB cameras, 3D Lidar, IMU, robot odometry, and pose information with efficient learning-based perception and planning algorithms that can execute on edge computing hardware. Our system uses a scene-aware switching method to perceive the environment for navigation at any time instant and dynamically switches between multiple perception algorithms. We test our system in a variety of sloped, rocky, muddy, and densely vegetated terrains and demonstrate its performance on Husky and Spot robots.