We study the generic dipole interaction of a monochromatic free-space electromagnetic field with a bi-isotropic nanoparticle or a molecule. Contributions associated with the breaking of dual, P, and T symmetries are responsible for electric-magnetic asymmetry, chirality, and the nonreciprocal magnetoelectric effect, respectively. We calculate absorption rates, radiation forces, and radiation torques for the nanoparticle and introduce novel field characteristics quantifying the transfer of energy, momentum, and angular momentum due to the three symmetry-breaking effects. In particular, we put forward a concept of "magnetoelectric energy density," quantifying the local PT symmetry of the field. Akin to the "superchiral" light suggested recently for local probing of molecular chirality, here we suggest employing complex fields for a sensitive probing of the nonreciprocal magnetoelectric effect in nanoparticles or molecules.