The development of multifunctional adhesive with high bond strength, toughness, mildew resistance, antibacterial properties, flame retardancy, and electromagnetic (EMI) shielding properties has drawn interest and simultaneously presents a challenge in the wood panel industry. Herein, inspired by the organic–inorganic hybrid structure of oysters, an antibacterial agent quaternary ammonium salted hyperbranched polyamide (QHBPA), was synthesized to modify graphene nanosheets (GNSs) via cation-π interaction, eventually forming a G-co-Q hybrid. The G-co-Q hybrid was then combined with soy protein isolate (SPI) and phytic acid (PA) to develop a plywood adhesive with an organic–inorganic hybrid structure via electrostatic interactions and hydrogen bonds. The resultant adhesive exhibited good mildew resistance and antibacterial activity (144 h shelf life). Compared with the SPI adhesive, the dry and wet shear strengths of the plywood with the SPI/PA/G-co-Q adhesive increased by 76.6% and 78.7%, respectively. Meanwhile, non-covalent cross-linking and the formation of an organic–inorganic hybrid structure endowed the adhesive with excellent toughness. Furthermore, the limiting oxygen index (LOI) of the resultant adhesive was 35.5%, reflecting an increase of 49.1% relative to that of the SPI adhesive, indicating that the adhesive possesses superior flame retardancy. Importantly, owing to its unique isolated multilayered structure, the plywood bonded by our adhesive is an absorption dominated EMI shielding material with low reflection characteristics and displays a desirable EMI shielding effectiveness of 43 dB. Therefore, this study provides a creative insight into the design of high value-added and multifunctional plywood with promising application prospects not only in conventional wood-based panels but also in advanced EMI shielding materials.