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. Belongs to the prokaryotic molybdopterin-containing oxidoreductase family.