Excited states and energy relaxation processes are studied for stacked InAs/GaAs QD's with GaAs cap layers grown by migration enhanced epitaxy. Photoluminescence excitation (PLE) spectra reveal the excited state spectrum as a function of size for self-assembled InAs QD's in multilayered samples with 36-ML spacers. The observed energy shifts and splittings are consistent with those of hole states numerically calculated for pyramidal QD's supporting assignment to the transition between the electron ground |000〉 and the |001〉 excited hole state. The optical results suggest the island shape uniformity to improve in multilayered samples, which is attributed to the contribution of the buried islands to the surface strain altering the island formation kinetics and energetics that also underlie vertical self-organization. Time-resolved photoluminescence (TRPL) results yield a lifetime of 40 ps for the first excited |001〉 hole state, attributed to multiphonon relaxation processes bridging the approximately 100 meV level separation, and ground-state lifetimes around 700 ps independent of the detection energy. At high excitation densities saturation of QD states leads to long-living excited-state PL and up to 1 ns delay in the ground-state PL decay, showing radiative decay to be the dominant recombination process in the QD's. The results presented contribute to the understanding of PLE spectra of an inhomogeneous QD ensemble, which is argued to be sensitive to the shape uniformity, the excited-state spectrum, and competing recombination processes.