Using a high-sensitivity torsional oscillator (TO) technique, we mapped the rotational and relaxational dynamics of solid helium-4 (4He) throughout the parameter range of the proposed supersolidity. We found evidence that the same microscopic excitations controlling the torsional oscillator motions are generated independently by thermal and mechanical stimulation. Moreover, a measure for the relaxation times of these excitations diverges smoothly without any indication for a critical temperature or critical velocity of a supersolid transition. Finally, we demonstrated that the combined temperature-velocity dependence of the TO response is indistinguishable from the combined temperature-strain dependence of the solid's shear modulus. This implies that the rotational responses of solid 4He attributed to supersolidity are associated with generation of the same microscopic excitations as those produced by direct shear strain.