We apply photodetachment-photoelectron spectroscopy to measure the electron affinities and the energetics of the lowest excited electronic states of the neutral molecules para-terphenyl (p3P), para-quaterphenyl (p4P) and para-quinquephenyl (p5P), including especially the triplet states below S1. The interpretation of the experimental data is based on the comparison to calculated 0-0 energies and Dyson norms, using density functional theory and multireference configuration interaction methods, as well as Franck-Condon patterns. The comparison between calculated and experimental vibrational fine-structures reveals a twisted benzoid-like molecular structure of the S0 ground state and nearly planar quinoid-like nuclear arrangements in the S1 and T1 excited states as well as in the D0 anion ground state. For all para-oligophenylenes (ppPs) in this series, at least two triplet states have been identified in the energy regime below the S1 state. The large optical S0-S1 cross sections of the ppPs are rationalised by the nodal structure of the molecular orbitals involved in the transition. The measured electron affinities range from 380 meV (p3P) over 620 meV (p4P) to 805 meV (p5P). A saturation of the electron binding energy with the increasing number of phenyl units is thus not yet in sight.