We investigate the effect of illumination on the velocity of the ${\mathit{L}}_{\mathrm{\ensuremath{\perp}}}$ and ${\mathrm{FT}}_{\mathrm{\ensuremath{\perp}}}$ acoustic-wave propagation along layers of \ensuremath{\varepsilon}-GeSe [in the (0001) plane]. Frequency and temperature dependences and also relative changes of various acoustic-wave velocities under hydrostatic pressure in \ensuremath{\varepsilon}-GaSe are used to show that photosensitive absorption and the change of the ${\mathit{L}}_{\mathrm{\ensuremath{\perp}}}$ and ${\mathrm{FT}}_{\mathrm{\ensuremath{\perp}}}$ wave-propagation velocity are associated with the piezoelectric interaction of the acoustic wave with free charge carriers. High anisotropy of anharmonic properties at compressive and shearing strain of the layers relative to each other is a characteristic feature of lamellar crystals and is related to anisotropy of the crystal elasticity. The velocity of piezoactive acoustic waves in P6\ifmmode\bar\else\textasciimacron\fi{}m2 crystals has been calculated theoretically. Piezoelectric characteristics and Gr\"uneisen constants for the acoustic branches of the phonon spectrum in \ensuremath{\varepsilon}-GaSe have been determined.