Self-organized GaN/AlN stacked quantum dots (QDs) have been studied by means of cathodoluminescence (CL), near field scanning optical microscopy (NSOM), photoluminescence, mu-Raman, and transmission electron microscopy. Assignment of the optical emissions was made on the basis of the structural parameters, power-dependent optical studies and depth-resolved CL. Power-dependent studies allowed us to distinguish between quantum confined and buffer emissions. On increasing the power injection conditions, a QD-size-dependent blue shift due to the screening of the internal electric fields was found together with a trend to saturation observed in the high injection limit. The possible evidence of excited states has also been shown by power-dependent photoluminescence and CL. Different blue shifts in specimens with different numbers of stacked layers suggested possible different residual strain values as confirmed by mu-Raman studies. Depth-resolved CL investigations performed at constant power injection per unit volume allowed us to distinguish between QD layers with different nominal GaN coverages and a linear dependence of peak energy versus GaN monolayer number has also been found. Adding 1 ML of GaN resulted in an average shift of about 150 meV. The existence of QDs with different size distributions along the growth axis was also found. The observations were confirmed by NSOM spectroscopy.