The GASP survey, based on MUSE data, is unveiling the properties of the gas in the so-called `jellyfish' galaxies: these are cluster galaxies with spectacular evidence of gas stripping by ram pressure. In a previous paper (Poggianti et al.), we selected the seven GASP galaxies with the most extended tentacles of ionized gas, and based on individual diagnostic diagrams concluded that at least five of them present clear evidence for an active galactic nucleus. Here we present a more detailed analysis of the emission lines properties in these galaxies. Our comparison of several emission line ratios with both AGN and shock models show that photoionization by the AGN is the dominant ionization mechanism. This conclusion is strengthened by the analysis of H β luminosities, the presence of nuclear iron coronal lines, and extended (>10 kpc) emission line regions ionized by the AGN in some of these galaxies. From emission line profiles, we find the presence of outflows in four galaxies, and derive mass outflow rates, time-scales, and kinetic energy of the outflows.