Pneumatic oscillators, incorporating soft non-electrical logic gates, offer an efficient means of actuating robots to perform tasks in extreme environments. However, the current design paradigms for these devices typically feature uniform structures with low rigidity, which restricts their oscillation frequency and limits their functions. Here, we present a pneumatic hybrid oscillator that integrates a snap-through buckling beam, fabric chambers, and a switch valve into its hybrid architecture. This design creates a stiffness gradient through a soft-elastic-rigid coupling mechanism, which substantially boosts the oscillator's frequency and broadens its versatility in robotic applications. Leveraging the characteristic capabilities of the oscillator, three distinct robots are developed, including a bionic jumping robot with high motion speed, a crawling robot with a pre-programmed logic gait, and a swimming robot with adjustable motion patterns. This work provides an effective design paradigm in robotics, enabling autonomous and efficient execution of complex, high-performance tasks, without relying on electronic control systems.