Structures and properties are reported for p*-radical cations and for s*-radical cations and anions, containing SS, SN and SO odd-electron bonds, from a variety of ab initio molecular orbital techniques and Density Functional Theory (DFT). Characteristic frequencies and absorption bands are determined to aid in the assignment of transient vibrational and optical spectra detected in pulse radiolysis experiments. Hyperfine coupling tensors are evaluated to facilitate the identification of these radicals by EPR spectroscopy. By comparison with predictions from accurate coupled-cluster based calculations in some simple model systems, DFT is shown to have difficulties in correctly describing the electronic structure of these radical ions. Useful linear relationships are uncovered between the computed lenght of the odd-electron bond and both the wavelenght of maximum optical absorption and the bond stretching frequency.