Electric and magnetic dipole moments dominate the scattering properties of small nanoparticles in optics. Ordinarily, electric dipole moments are excited by the local electric field, and magnetic dipole moments by the magnetic field. Bi-anisotropy, or magneto-electric coupling, largely enriches the electromagnetic response of materials. Similarly, in acoustics the dominant scattering contributions from objects smaller than the wavelength, monopole and dipole moments, are commonly excited by pressure and velocity, respectively. The recent interest in Willis acoustic materials, for which these responses are coupled, leads us to analyze the opportunities offered by the analogues of bi-anisotropic nanoparticles in acoustics and their relevance in practical applications to tailor sound. We also present an extraction procedure to determine the acoustic polarizability tensor of an arbitrary object and relate its bi-anisotropic response to its geometry and material properties.