Abstract: Ground and isomeric states of the neutron-deficient odd-A isotopes 183Hg, 185Hg, and 187Hg are described from a microscopic calculation based on a self-consistent, axially deformed Hartree-Fock mean field with the Skyrme functional and pairing within BCS approximation. For each equilibrium shape and different odd-neutron states, results on mean-square charge radii and magnetic dipole moments are given and analyzed in the context of their sensitivity to the nuclear deformation and to the spin and parity. Spin-isospin correlations within proton-neutron quasiparticle random phase approximation are then introduced in the nuclear states to obtain the distributions of Gamow-Teller strength and the beta+/EC half-lives of these isotopes, whose measurements are planned at ISOLDE-CERN using total absorption gamma-ray spectroscopy techniques.