The fabrication of smart biocomposites from sustainable resources that could replace today’s petroleum-derived polymer materials is a growing field of research. Here, we report preparation of novel biocomposites using nanocellulose networks extracted from food residue (onion skin) and a vegetable oil-based bioresin. The resin was synthesized via the Diels-Alder reaction between furfuryl methacrylate and tung oil at various ratios of the components. The onion-skin-extracted cellulose nanofiber and cellulose nanocrystal networks were then impregnated with the resins yielding biocomposites that exhibited improved mechanical strength and higher storage modulus values. The properties of the resins, as well as biocomposites, were affected by the resin compositions. A 190–240-fold increase in mechanical strength was observed in the cellulose nanofiber (CNF) and cellulose nanocrystal (CNC)-reinforced biocomposites with low furfuryl methacrylate content. The biocomposites exhibited interesting shape-memory behavior with 80–96% shape recovery being observed after 7 creep cycles.