We present the photometric and spectroscopic analysis of three Type II supernovae (SNe): 2014cx, 2014cy, and 2015cz. SN 2014cx is a conventional Type IIP with shallow slope (0.2 mag/50 d) and an atypical short plateau (similar to 86 d). SNe 2014cy and 2015cz show relatively large decline rates (0.88 and 1.64 mag/50 d, respectively) at early times before settling to the plateau phase, unlike the canonical Type IIP/L SN light curves. All of them are normal luminosity SN II with an absolute magnitude at mid-plateau of M-V,14cx(50) = -16.6 +/- 0.4 mag, M-V,14cy(50) = -16.5 +/- 0.2 mag, and M-V,15cz(50) = -17.4 +/- 0.3 mag. A relatively broad range of Ni-56 masses is ejected in these explosions (0.027-0.070M(circle dot)). The spectra shows the classical evolution of SNe II, dominated by a blue continuum with broad H lines at early phases and narrower metal lines with PCygni profiles during the plateau. High-velocity H I features are identified in the plateau spectra of SN 2014cx at 11 600 kms(-1), possibly a sign of ejecta-circumstellar interaction. The spectra of SN 2014cy exhibit strong absorption profile of HI similar to normal luminosity events whereas strong metal lines akin to sub-luminous SNe. The analytical modelling of the bolometric light curve of the three events yields similar progenitor radii within errors (478, 507, and 660 R-circle dot for SNe 2014cx, 2014cy, and 2015cz, respectively), a range of ejecta masses (15.0, 22.2, and 20.6M(circle dot) for SNe 2014cx, 2014cy, and 2015cz), and a modest range of explosion energies (3.3-7.2 foe where 1 foe=10(51) erg).