Lattice sites and collective ordering of oxygen atoms in HgBa2CaCu2O6+delta were studied using the perturbed angular correlation (PAC) technique at ISOLDE/CERN. The electric field gradients (EFG) at Hg-199m nuclei have been measured as functions of oxygen doping on the Hg planes, above and below T-c. In comparison with the results obtained for oxygen and fluorine doping in Hg-1201, the analysis shows a different oxygen ordering exhibited by Hg-1212. Moreover, for all studied cases, the experimental results show that at a local scale there is non uniform oxygen distribution. A series of ab initio EFG calculations allowed to infer that at low concentrations, regions without oxygen coexist with regions where O-2 delta dumbbell molecules are located at the center of the Hg mesh. On the other side, at high concentrations, O-2 delta dumbbell molecules coexist with single O-delta atoms occupying the center of the Hg mesh. The present results suggest that oxygen sits on the Hg planes in the form of a molecule and not as a single atom.