Dynamic response of materials to high-speed and high-intensity loading conditions is important in several applications including high-speed flows with droplets, bubbles and particles, and hyper-velocity impact and penetration processes. In such high-pressure physics problems, simulations encounter challenges associated with the treatment of material interfaces, particularly when strong nonlinear waves like shock and detonation waves impinge upon them. To simulate such complicated interfacial dynamics problems, a fixed Cartesian grid approach in conjunction with levelset interface tracking is attractive. In this regard, a sharp interface Cartesian grid-based, Ghost Fluid Method (GFM) is developed for resolving embedded fluid, elasto-plastic solid and rigid (solid) objects in hyper-velocity impact and high-intensity shock loaded environment. The embedded boundaries are tracked and represented by virtue of the level set interface tracking technique. The evolving multi-material interface and the flow are coupled by meticulously enforcing the boundary conditions and jump relations at the interface. In addition, a tree-based Local Mesh Refinement scheme is employed to efficiently resolve the desired physics. The framework developed is generic and is applicable to interfaces separating a wide range of materials and for a broad spectrum of speeds of interaction (O(km/s)). The wide repertoire of problems solved in this work demonstrates the flexibility, stability and robustness of the method in accurately capturing the dynamics of the embedded interface. Shocks interacting with large ensembles of particles are also computed.