The CrVO4-type magnetic oxides MM'O-4 consist of edge-sharing MO4 octahedral chains condensed with M'O-4 tetrahedra and exhibit a wide variety of magnetic structures. The magnetic properties of these oxides were examined by studying their spin exchange interactions on the basis of spin dimer analysis. The nature and magnitudes of the intra- and interchain spin exchange interactions depend on the square-to-rectangle distortion in the basal planes of the MO4 chain and on the difference between the M 3d and O 2p orbital energies. The spiral magnetic structures of beta-CrPO4 and MnSO4 originate from the pseudohexagonal arrangement of the MO4 chains and the frustrated interchain antiferromagnetic interactions.