A universal effective NN interaction SkE of the Skyrme type has been proposed, suitable for both ground and excited states in nuclei throughout the nuclear mass table. In this second part (II) the behaviour of the SkE force as a particle-particle and particle-hole effective interaction is studied. We show the ability of SkE to reproduce all two-particle (two-hole) valence nucleon spectra. A detailed study for 18O and 130Sn is carried out. The definitely determined SkE interaction is also applied as a particle-hole interaction and detailed shell-model calculations for the light 16O and heavy 208Pb nuclei are discussed. We also concentrate on the description of giant multipole resonances throughout the whole nuclear mass region.