We report the pronounced effects of oxygen growth pressure (0.13 Pa-40 Pa) on the surface morphology, hydrophobicity, structural, optical and electrical properties of ZnO and aluminium-doped ZnO (AZO) thin films deposited by room temperature pulsed-laser deposition on the low water-absorbing polymer Zeonor. Significant changes were observed for oxygen growth pressures below ~ 10 Pa. In this pressure range, the morphology changed from nanocrystalline to that of a continuous film with a shift of the growth orientation of the crystalline fraction of the deposit from c-plane to m-plane. The appearance of valley-shaped surface cracks caused a significant increase of rms surface roughness, reduced hydrophobicity and shift to hydrophilicity at 0.13 Pa. The visible optical transmittance of the film reduced from an average of 90 % to 65 % and the orange/red deep level emission was quenched. The electrical properties showed decreasing resistivities (105 Ω cm to 10-3 Ω cm) and Hall mobilities (35 cm2/V-s to 3 cm2/V-s) and increasing carrier concentrations (1011 cm-3 to 1021 cm-3). These significant changes of the films physical characteristics were related to the morphological and structural changes induced by the change of oxygen growth pressure. The observed effects are interesting for applications in flexible optoelectronics and briefly discussed in this context.