Small water clusters, (H₂O)₂₀ and (H ₂O)₂₆, containing charged (Li⁺) and neutral (atomic Li and methane) particles, have been studied using molecular dynamics simulations at temperatures ranging from 10 to 200 K. Transitions between solid and liquid phases were investigated in relation to inserted particle charge and size, as well as the initial cluster configuration. It was found that embedding the methane molecule inside a dodecahedral (H₂O)₂₀ cage significantly stabilizes the cluster configuration. Nevertheless, the melting temperature of the CH₄(H₂O)₂₀ cluster is reduced by methane. This system does not underwent an additional polymorphic structural transformation typical for the pure water dodecahedron, resulting in lower total energy. In the case of the 3 × 3 × 3 cubic-ice aggregate the enclosure of a neutral molecule also leads to a stabilization of the cluster structure and the melting temperature of CH₄(H ₂O)₂₆ or Li⁰(H₂O)₂₆ aggregates raises. However, the main features of the overall phase evolution are mainly determined by water-water interactions.