The ability to control electrical properties and magnetism by varying the crystal structure using the effect of the A-site cation in oxygen deficient perovskites has been studied in AA'Fe2O6-delta, where A = Sr, Ca and A' = Sr. The structure of Sr2Fe2O6-delta, synthesized at 1250 degrees C in air, contains dimeric units of FeO5 square pyramids separated by FeO6 octahedra. Here we show that this ordering scheme can be transformed by changing the A-site cations from Sr to Ca. This leads to a structure where layers of corner-sharing FeO6 octahedra are separated by chains of FeO4 tetrahedra. Through systematic variation of the A-site cations, we have determined the average ionic radius required for this conversion to be similar to 1.41 angstrom. We have demonstrated that the magnetic structure is also transformed. The Sr-2 compound has an incommensurate magnetic structure, where magnetic moments are in spin-density wave state, aligning perpendicular to the body diagonal of the unit cell. With the aid of neutron diffraction experiments at 10 and 300 K, we have shown that the magnetic structure is converted into a long-range G-type antiferromagnetic system when one Sr is replaced by Ca. In this G-type ordering scheme, the magnetic moments align in the 001 direction, antiparallel to their nearest neighbors. We have also performed variable-temperature electrical conductivity studies on these materials in the temperature range 298-1073 K. These studies have revealed the transformation of charge transport properties, where the metallic behavior of the Sr-2 compound is converted into semiconductivity in the CaSr material. The trend of conductivity as a function of temperature is reversed upon changing the A site cation. The conductivity of the Sr-2 compound shows a downturn, while the conductivity of the CaSr material increases as a function of temperature. We have also shown that the CaSr compound exhibits temperature-dependent behavior typical of a mixed ionic-electronic conducting system.