The Virgo cluster of galaxies provides excellent conditions for studying interactions of galaxies with the cluster environment. Both the high-velocity tidal interactions and effects of ram pressure stripping by the intracluster gas can be investigated in detail. We extend our systematic search for possible anomalies in the magnetic field structures of Virgo cluster spirals in order to characterize a variety of effects and attribute them to different disturbing agents. Six angularly large Virgo cluster spiral galaxies (NGC4192, NGC4302, NGC4303, NGC4321, NGC4388, and NGC4535) were targets of a sensitive total power and polarization study using the 100-m radio telescope in Effelsberg at 4.85GHz and 8.35GHz (except for NGC4388 observed only at 4.85GHz, and NGC4535 observed only at 8.35GHz). Magnetic field structures distorted to various extent are found in all galaxies. Three galaxies (NGC4302, NGC4303, and NGC4321) show some signs of possible tidal interactions, while NGC4388 and NGC4535 have very likely experienced strong ram-pressure and shearing effects, respectively, visible as distortions and asymmetries of polarized intensity distributions. As in our previous study, even strongly perturbed galaxies closely follow the radio-far-infrared correlation. In NGC4303 and NGC4321, we observe symmetric spiral patterns of the magnetic field and in NGC4535 an asymmetric pattern. Magnetic fields allow us to trace even weak interactions that are difficult to detect with other observations. Our results show that the degree of distortions of a galaxy is not a simple function of the distance to the cluster center but reflects also the history of its interactions. The angle between the velocity vector and the rotation vector of a galaxy may be a general parameter that describes the level of distortions of galactic magnetic fields.