This paper presents a soft gripper system in which actuation, sensing, and signal processing are all realized using soft dielectric elastomer (DE) devices. The platform integrates three functional units: a multilayer dielectric elastomer actuator (DEA) module that drives a compliant two-finger gripper, two tactile sensors mounted on the fingertips for contact detection and coarse shape recognition, and a dielectric elastomer switch (DES) that enables soft electronics control. The DEA module consists of eight parallel multilayer actuators, each comprising four active layers and a nonlinear biasing spring to amplify stroke, and is powered by an embedded high-voltage supply operated at 3 kV. The DES operates by mechanically modulating the resistance of a stretchable piezoresistive electrode, providing reliable switching behavior under high voltage. Grasping tests demonstrate that the system achieves a maximum opening angle of 38° and can safely manipulate delicate objects, including cherries and eggs, without damage. These results demonstrate the feasibility of advancing toward fully soft robotic systems by integrating DE-based components for actuation, sensing, and signal processing.