Four (BEDT-TTF)4A[M(C2O4)3]·DMF (DMF = dimethylformamide) salts of the organic donor molecule bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF) with metal oxalate anions, where A = (NH4, K), M = Cr (1); A = NH4, M = Fe (2); A = K, M = Cr (3); and A = NH4, M = Cr (3′) were prepared by electrocrystallization. These salts were characterized by single-crystal X-ray diffraction, electron spin resonance (ESR) spectroscopy, electrical resistance measurements, and electronic band structure calculations. The structures (with space group C2/c) consist of alternating β″-type layers of BEDT-TTF and an approximately hexagonal network formed by the A+ cation and the metal, with the solvent molecule, DMF, occupying hexagonal cavities in the anion layer. All of the salts are two-dimensional organic metals down to 4.2 K and do not exhibit superconductivity. Their electronic band structure is similar to that of the known organic superconductor β″-(BEDT-TTF)4H3O[Fe(C2O4)3]·BN. The ESR spectra of salts 1 and 3′ are characterized by two resonances, one of Gaussian shape arising from the 3d localized electrons of Cr3+ and the other of Lorentzian (and Dysonian) shape due to the conduction electrons in the organic layers. On the basis of the calculated Fermi surfaces it is suggested that these salts could exhibit an interesting magnetoresistance behavior if disorder does not prevent the observation of the Shubnikov-de Haas oscillations.