Lightweight, compressible and highly sensitive pressure/strain sensing materials are highly desirable for the development of health monitoring, wearable devices and artificial intelligence. Herein, a very simple, low-cost and solution-based approach is presented to fabricate versatile piezoresistive sensors based on conductive polyurethane (PU) sponges coated with synergistic multiwalled carbon nanotubes (MWCNTs) and graphene. These sensor materials are fabricated by convenient dip-coating layer-by-layer (LBL) electrostatic assembly followed by in situ reduction without using any complicated microfabrication processes. The resultant conductive MWCNT/RGO@PU sponges exhibit very low densities (0.027-0.064 g cm-3), outstanding compressibility (up to 75%) and high electrical conductivity benefiting from the porous PU sponges and synergistic conductive MWCNT/RGO structures. In addition, the MWCNT/RGO@PU sponges present larger relative resistance changes and superior sensing performances under external applied pressures (0-5.6 kPa) and a wide range of strains (0-75%) compared with the RGO@PU and MWCNT@PU sponges, due to the synergistic effect of multiple mechanisms: "disconnect-connect" transition of nanogaps, microcracks and fractured skeletons at low compression strain and compressive contact of the conductive skeletons at high compression strain. The electrical and piezoresistive properties of MWCNT/RGO@PU sponges are strongly associated with the dip-coating cycle, suspension concentration, and the applied pressure and strain. Fully functional applications of MWCNT/RGO@PU sponge-based piezoresistive sensors in lighting LED lamps and detecting human body movements are demonstrated, indicating their excellent potential for emerging applications such as health monitoring, wearable devices and artificial intelligence.