We present a magnetophotoluminescence study on neutral and charged excitons confined to InAs/GaAs quantum dots. Our investigation relies on a confocal microscope that allows arbitrary tuning of the angle between the applied magnetic field and the sample growth axis. First, from experiments on neutral excitons and trions, we extract the in-plane and on-axis components of the Landé tensor for electrons and holes in the s shell. Then, based on the doubly negatively charged exciton magnetophotoluminescence, we show that the p-electron wave function spreads significantly into the GaAs barriers. We also demonstrate that the p-electron g factor depends on the presence of a hole in the s shell. The magnetic field dependence of triply negatively charged excitons photoluminescence exhibits several anticrossings, as a result of coupling between the quantum dot electronic states and the wetting layer. Finally, we discuss how the system evolves from a Kondo-Anderson exciton description to the artificial atom model when the orientation of the magnetic field goes from Faraday to Voigt geometry.