Dilatonic black hole dyon solutions with an arbitrary dilatonic coupling constant λ ≠ 0 and canonical sign ε = +1 for the scalar field kynetic term are considered. These solutions are defined up to solutions of two master equations for moduli functions. For λ ≠ 1/2 the solutions are extended to ε = ±1, where ε = -1 corresponds to a ghost (phantom) scalar field. Some physical parameters of the solutions: gravitational mass, scalar charge, Hawking temperature, black hole area entropy and parametrized post-Newtonian (PPN) parameters β and γ are obtained. It is shown that PPN parameters do not depend on scalar field coupling λ and ε. Two groups of bounds on gravitational mass and scalar charge (for a fixed and arbitrary extremality parameter μ > 0) are found by using a certain conjecture on parameters of solutions when1 + 2λ2ε > 0. These bounds are verified numerically for certain examples. Using the product we are led to the well-known lower bound on mass which was obtained earlier by Gibbons, Kastor, London, Townsend and Traschen by using spinor techniques. © 2015 IOP Publishing Ltd.