The present work reports the results of the MP2/6-31+G(d,p) study of the interaction between CH4 and (H2O)(2) and H5O2+, including the optimized geometries of the stable structures, their harmonic vibrational frequencies, total energies with the two- and three-body contributions, and natural charges. Three stable structures exist on the potential energy surface of the CH4.(H2O)(2) complex formed via a CH...O hydrogen bond. Under its formation, the corresponding CH bond undergoes a small contraction, resulting in a blue shift of the corresponding v(CH) vibration. One of the structures, resembling a cyclic trimer with relatively short distances between two hydrogen atoms of CH4 and the terminal hydrogen atom of (H2O)(2), is characterized by the largest total and the largest two-body interaction energies. This suggests the existence of a weak attractive interaction between the three hydrogen atoms. To shed light on the nature of such an interaction between three hydrogen atoms, we study the complex between CH4 and H5O2+ and demonstrate that its formation originates from a substantially stronger interaction between three hydrogen atoms and induces a marked asymmetry of the central (O...H...O) hydrogen bond of the cation. The distances between two hydrogen atoms of CH4 and one of the terminal hydrogen atoms of H5O2+ are very short (1.87 Angstrom), implying that these three hydrogen atoms interact with each other due to a relatively strong ionic multi-dihydrogen bonding.