Soft actuators that undergo programmable shape change in response to a stimulus are enabling components of future soft robots and other soft machines. Strategies to power these actuators often require the incorporation of rigid, electrically conductive materials into the soft actuator, thus limiting the compliance and shape change of the material. In this study, we develop a 4D-printable composite composed of liquid crystal elastomer (LCE) matrix with dispersed droplets of eutectic gallium indium alloy (EGaIn). Using deformable EGaIn droplets in place of rigid conductive fillers preserves the compliance and shape-morphing properties of the LCE. The process enables 4D-printed LCE actuators capable of photothermal and electrothermal actuation. At low liquid metal (LM) concentrations (71 wt %), the composite actuator exhibits a photothermal response upon irradiation of near-IR light. Printed actuators with a twisted nematic configuration are capable of bending angles of 150 at 800 mW cm-2. At higher LM concentrations (88 wt %), the embedded LM droplets can form percolating networks that conduct electricity and enable electrical Joule heating of the LCE. Actuation strain ranging from 5 to 12% is controlled by the amount of electrical power that is delivered to the composite. We also introduce a method for multimaterial printing of monolithic structures where the LM filler loading is spatially varied. These multifunctional materials exhibit innate responsivity where the actuator behaves as an electrical switch and can report one of two states (on/off). These multiresponsive, 4D-printable composites enable multifunctional, mechanically active structures that can be powered with IR light or low DC voltages.