Catalyzes the reduction of dimethyl sulfoxide (DMSO) and trimethylamine N-oxide (TMAO) to dimethyl sulfide (DMS) and trimethylamine, respectively. The terminal DMSO reductase can also use various sulfoxides and N-oxide compounds as terminal electron acceptor in addition to DMSO and TMAO. a menaquinone + dimethyl sulfide + H2O = a menaquinol + dimethyl sulfoxide 2 Fe(III)-[cytochrome c] + H2O + trimethylamine = 2 Fe(II)-[cytochrome c] + 3 H(+) + trimethylamine N-oxide Binds 1 molybdenum-bis(molybdopterin guanine dinucleotide) (Mo-bis-MGD) cofactor per subunit. Homodimer. Predicted to be exported by the Tat system. The position of the signal peptide cleavage has been experimentally proven. Disruption of dmsA results in the inability to use DMSO or TMAO as the terminal electron acceptor in anaerobic respiration and in greatly diminished in vitro DMSOR activity. Belongs to the prokaryotic molybdopterin-containing oxidoreductase family.