Correlated quantum-chemical calculations are performed on phenylenevinylene oligomers containing up to eleven repeat units, to characterize the nature of the electronic excitations relevant for the photophysical properties of the corresponding polymer. The focus is first on the nonlinear optical response of model conjugated chains and the simulation of their frequency-dependent (third-harmonic generation, electroabsorption, and two-photon absorption) response. From the assignment of the calculated resonance features, the excited states dominating the third-order nonlinear polarizability are identified and their chain-length dependence is investigated. On that basis, we build an essential-state single-chain model (that includes the 1B(u), 2A(g), mA(g), and nB(u) states) and apply it to the interpretation of recent experimental data reported for poly(paraphenylenevinylene) and derivatives. We then examine how the exciton binding energy, here defined as the difference between the energies of the charge-separated nB(u) and the strongly optically allowed 1B(u) excited states, is affected by both intrachain and interchain polarization effects.