Polymer composites are widely utilized in industries such as electronics and communications due to their lightweight nature, strength, and enhanced functionality. Among them, liquid metal polymer composites (LMPCs) offer a unique blend of mechanical and electrical properties by incorporating fillers like galinstan (a room temperature liquid metal alloy of gallium, indium and tin), which exhibits both metallic conductivity and fluidity in an addition to a solid oxide shell that acts as an interfacial stabilizer. When dispersed into an elastomer, galinstan exhibits characteristics of both solid and liquid fillers due to the unique contributions of the polymer matrix, oxide shell, and bulk liquid metal components. This study investigates the distinct mechanical properties of LMPCs under tensile, compressive, and torsional loading. The findings in this work challenge commonly held assumptions about the uniformity of modulus behavior across deformation modes, emphasizing the need to consider deformation specific behavior. For example, tensile and torsional behavior aligns with classical mechanical models, such as Eshelby's inclusion theory, while compressive behavior remains less predictable. A complex relationship between liquid metal concentration and compressive modulus is observed, diverging from trends seen in tensile and torsional modes and what would classically be expected when considering mechanical or energetic contributions. Through a combined experimental and modeling approach, this work explores the contributions of the oxide shell and interfacial energy to LMPC performance under these three loading modes. The findings support the development of optimized material designs and enhanced performance in functional applications such as stretchable electronics.