Biological membranes with specific mechanical properties are essential for numerous cellular functions, such as endocytosis, metabolism, and intracellular trafficking, which rely on precise control of membrane shape. In living systems, membrane morphology is co-regulated by curvature-sensing proteins and osmotic pressure. However, the mechanical interplay among these two factors and the membrane itself during deformation remains poorly understood. To address this, we employed dynamic triangulation Monte Carlo simulations to study membrane vesicles embedded with multiple curvature-inducing proteins under osmotic pressure. This stochastic approach captures key microscopic behaviors, including membrane fluctuations, protein diffusion, and vesicle shrinkage. A comparative analysis reveals cooperative effects of osmotic pressure and curved proteins on vesicle morphology, which depend strongly on membrane mechanics. For elastic membranes, osmotic pressure alone induces concave shapes, while curvature proteins generate rough, quasi-spherical structures; together, they synergistically form highly folded morphologies with low volume-to-area ratios. In fluid membranes, osmotic pressure suppresses protein-driven tubulation by increasing membrane tension. We identify diverse dynamic and equilibrium configurations as functions of solute concentration, protein curvature, and membrane mechanics, consistent with previous studies. These results offer a mechanical perspective on how osmotic pressure and curvature-sensing proteins jointly regulate vesicle deformation.