A multilayered composite structure formed by a random stacking of graphene oxide (GO) platelets is an attractive candidate for novel applications in nanoelectromechanical systems and paper-like composites. We employ molecular dynamics simulations with reactive force fields to elucidate the structural and mechanical properties of GO paper-like materials. We find that the large-scale properties of these composites are controlled by hydrogen bond networks that involve functional groups on individual GO platelets and water molecules within the interlayer cavities. Water content controls both the extent and collective strength of these interlayer hydrogen bond networks, thereby affecting the interlayer spacing and elastic moduli of the composite. Additionally, the chemical composition of the individual GO platelets also plays a critical role in establishing the mechanical properties of the composite--a higher density of functional groups leads to increased hydrogen bonding and a corresponding increase in stiffness. Our studies suggest the possibility of tuning the properties of GO composites by altering the density of functional groups on individual platelets, the water content, and possibly the functional groups participating in hydrogen bonding with interlayer water molecules.