The series La2-xSrxCoIrO6 is a suitable model system to investigate the effect of structural and chemical degrees of freedom on the resulting physical properties of double perovskites. Depending on the temperature and composition the following sequence of phase transitions is observed in this series: P21/n ↔ P21/n + I2/m ↔ I2/m ↔ I4/m ↔ Fm-3m. Whereas the phase transition between the monoclinic phases is of first order, the phase transitions between monoclinic (I2/m) and tetragonal and between tetragonal and cubic phases are of second order in nature. Changes in the oxidation states of both Co from Co2+ to Co3+ and Ir from Ir4+ to Ir5+ are concluded from the variation of the Co-O and Ir-O bond lengths, trends within the Bader charges, bond valence sums (BVS) and atomic sphere integration. Whereas Ir4+→Ir5+ takes place gradually within the P21/n phase and does not change significantly in the I2/m phase, the Co2+→Co3+ takes place abruptly in the I2/m phase at the phase boundary of P21/n/I2/m at x=1.5. Concerning the magnetic structures, three different types of them are discussed with respect to electronic structure calculations. With increasing Sr substitution, there is a transition from a stronger nearest neighbour (NN) AFM exchange interaction for x=1 to a stronger next nearest neighbour (NNN) AFM exchange interaction for x≥1. Competing interactions lead to NCM, most pronounced in La2CoIrO6. With increasing Sr-content, however, the ferromagnetic components are considerably reduced, so that the collinear approximations become more and more appropriate with increasing x. A reduction of the band gap is established with increasing Sr-content from 0.26 eV for x=0 to 0.05 for x=1.5, and a significant influence of B/B’-site cation disorder on the electronic transport properties is proposed based on the results for Sr2(Co0.85Ir0.15)(Ir0.85Co0.15)O6 (x=2). These gaps are the consequence of strongly correlated motion of the electrons due to strong onsite electron-electron Coulomb repulsion, which is confirmed by the fact that the band gap in the DOS could only be realized by applying an additional orbital dependent potential term U for the correlated 3d and 5d orbitals. Special attention is diverted towards La2CoIrO6. For this composition electronic structure calculations were performed for both AFM and FM configurations, which gave very similar total energies and thus support NCM by a sensitive preference of one of the possible states. Spin reorientation transition are found in single crystals of La2CoIrO6, which could be attributed to local minima in the angular dependence of the total energy, calculated from the non collinear arrangement of the magnetic moments of cobalt using the software code WIENNCM. The band gaps and d-band occupations are almost similar to the reported ones for collinear configurations. The above results are compared with the system La2-xCaxCoIrO6, which has only the band filling degree of freedom due to similar ionic radii of La3+ and Ca2+. But single phase samples were obtained only for x≤0.75. The most significant similarity between the systems is the magnetic phase transition from dominant NN AFM interaction to NNN AFM interaction. But they differ in the change of the oxidation states of Co and Ir upon Sr/Ca substitution. Especially the reduction of the band gap upon Sr substitution is attributed to the size degree of freedom, which influences the bandwidth of 3d Co and 5d Ir, whereas the band gap hardly changes through low level hole doping upon Ca substitution. The low level hole doping seems to be not enough the reduce the electron-electron repulsion significantly, as the bandwidth is limited by the eliminated size degree of freedom in the LaCa system (which is almost constant as the Co-O-Ir bond angles are almost constant) upon Ca substitution.