The extended optical theorem is generalized for scalar acoustical beams of arbitrary character with any angle of incidence interacting with an object of arbitrary geometric shape and size, and placed randomly in the beam's path with any scattering angle. Analytical expressions for the extinction, absorption, and scattering cross sections are derived, and the connections with the axial (i.e., along the direction of wave propagation) torque and radiation force calculations are discussed. As examples to illustrate the analysis for a viscoelastic object, the extinction, absorption, and scattering cross sections are provided for an infinite plane progressive wave, infinite nondiffracting Bessel beams, a zero-order spherical quasi-Gaussian beam, and a Bessel-Gauss vortex beam emanating from a finite circular aperture, which reduces to a finite high-order Bessel beam, a finite zero-order Bessel beam, and a finite piston radiator vibrating uniformly with appropriate selection of beam parameters. The similarity with the asymptotic quantum inelastic cross sections is also mentioned.