We apply a convenient parametrization of all Plebański-Demiański black holes of algebraic type D with the Kerr rotation, NUT twist, acceleration, electric and magnetic charges, and any value of the cosmological constant Λ, recently found by Astorino. This represents a complete class of exact solutions to the Einstein-Maxwell-Λ equations such that the (non-null) electromagnetic field is aligned with both the (geodesic, shear-free, double) principal null directions of the Weyl tensor. We derive a novel appropriate metric form and the corresponding canonical frames naturally adapted to both the de Sitter-like (Λ > 0) and the anti-de Sitter-like (Λ < 0) conformal infinity, and we demonstrate that these geometric objects are useful for investigation of radiation properties. In particular, using the Fernández-Alvarez-Senovilla criterion, it confirms that the gravitational radiation is present if, and only if, these black holes are accelerating.