Context : Core-collapse Supernovae ( CC-SNe ) descend from progenitors more massive than about 8 M _ { \odot } . Because of the young age of the progenitors , the ejecta may eventually interact with the circumstellar medium ( CSM ) via highly energetic processes detectable in the radio , X–ray , ultraviolet ( UV ) and , sometimes , in the optical domains . Aims : In this paper we present ultraviolet , optical and near infrared observations of five type II SNe , namely SNe 2009dd , 2007pk , 2010aj , 1995ad , and 1996W . Together with few other SNe they form a group of moderately luminous type II events . We investigate the photometric similarities and differences among these bright objects . We also attempt to characterise them by analysing the spectral evolutions , in order to find some traces of CSM-ejecta interaction . Methods : We collected photometry and spectroscopy with several telescopes in order to construct well-sampled light curves and spectral evolutions from the photospheric to the nebular phases . Both photometry and spectroscopy indicate a degree of heterogeneity in this sample . Modelling the data of SNe 2009dd , 2010aj and 1995ad allows us to constrain the explosion parameters and the properties of the progenitor stars . Results : The light curves have luminous peak magnitudes ( -16.95 < M _ { B } < -18.70 ) . The ejected masses of ^ { 56 } Ni for three SNe span a wide range of values ( 2.8 \times 10 ^ { -2 } M _ { \odot } < M ( ^ { 56 } Ni ) < 1.4 \times 10 ^ { -1 } M _ { \odot } ) , while for a fourth ( SNÂ 2010aj ) we could determine a stringent upper limit ( 7 \times 10 ^ { -3 } M _ { \odot } ) . Clues of interaction , such as the presence of high velocity ( HV ) features of the Balmer lines , are visible in the photospheric spectra of SNe 2009dd and 1996W . For SNÂ 2007pk we observe a spectral transition from a type IIn to a standard type II SN . Modelling the observations of SNe 2009dd , 2010aj and 1995ad with radiation hydrodynamics codes , we infer kinetic plus thermal energies of about 0.2–0.5 foe , initial radii of 2–5 \times 10 ^ { 13 } cm and ejected masses of \sim 5.0–9.5 M _ { \odot } . Conclusions : These values suggest moderate-mass , super-asymptotic giant branch ( SAGB ) or red super-giants ( RSG ) stars as SN precursors , in analogy with other luminous type IIP SNe 2007od and 2009bw .