In two of the latest experimental advances in the field of two-dimensional (2D) materials, penta-PdPS and -PdPSe layered materials have been fabricated. Inspired by these accomplishments, herein first-principles calculations are employed to explore the direction-dependent key physical properties of the PdPX (X = S, Se, Te) monolayers. Our results indicate that the PdPS, PdPSe, and PdPTe monolayers are indirect semiconductors, with HSE06 band gaps of 2.13, 1.89, and 1.37 eV, respectively. Optical calculations reveal that the first absorption peaks of these novel monolayers along the in-plane polarizations are located in the visible range of light. Moreover, it is predicted that the PdPSe monolayer yields suitable valence and conduction band edge positions for visible-light-driven water splitting reactions. Our results confirm the decline of elastic modulus, tensile strength, phonons’ group velocity, and lattice thermal conductivity with the increase of the atomic weight of chalcogen atoms in PdPX nanosheets. It is furthermore shown that these novel 2D systems exhibit anisotropic mechanical, optical, and heat conduction properties. The obtained first-principles results provide a comprehensive vision about the critical physical properties of the PdPX (X = S, Se, Te) nanosheets and highlight their prospect for nanoelectronics, optoelectronics, and energy conversion applications.