Soft conductive materials should enable large deformation while keeping high electrical conductivity and elasticity. The graphene oxide (GO)-based sponge is a potential candidate to endow large deformation. However, it typically exhibits low conductivity and elasticity. Here, the highly conductive and elastic sponge composed of GO, flower-shaped silver nanoparticles (AgNFs), and polyimide (GO-AgNF-PI sponge) are demonstrated. The average pore size and porosity are 114 µm and 94.7%, respectively. Ag NFs have thin petals (8–20 nm) protruding out of the surface of a spherical bud (300–350 nm) significantly enhancing the specific surface area (2.83 m2 g−1). The electrical conductivity (0.306 S m−1 at 0% strain) of the GO-AgNF-PI sponge is increased by more than an order of magnitude with the addition of Ag NFs. A nearly perfect elasticity is obtained over a wide compressive strain range (0–90%). The strain-dependent, nonlinear variation of Young's modulus of the sponge provides a unique opportunity as a variable stiffness stress sensor that operates over a wide stress range (0–10 kPa) with a high maximum sensitivity (0.572 kPa−1). It allows grasping of a soft rose and a hard bottle, with the minimal object deformation, when attached on the finger of a robot gripper.