We have measured the quadratic electroabsorption (EA) spectrum of a variety of soluble luminescent and nonluminescent \ensuremath{\pi}-conjugated polymer films in the spectral range of 1.5--4.5 eV. The luminescent polymers include MEH and DOO derivatives of poly(phenylene-vinylene), poly(phenylene ethylene), and polythiophene; the nonluminescent polymers include poly(diethynyl silane) and monosubstituted polyacetylene. All EA spectra show a Stark shift of the low-lying odd-parity exciton ${(1B}_{u})$ and imply the presence of phonon sidebands. There are also higher-energy bands due to transfer of oscillator strength to even-parity exciton states ${(A}_{g}),$ the strongest of which ${(mA}_{g})$ is located at an energy about 1.3 times that of the ${1B}_{u}$ exciton in both luminescent and nonluminescent polymers; in the luminescent polymers the EA spectra also show a second prominent ${A}_{g}$ state ${(kA}_{g})$ at an energy of about 1.6 times that of the ${1B}_{u}.$ We have successfully fitted the EA spectra by calculating the imaginary part of the third order optical susceptibility, $\mathrm{Im}[{\ensuremath{\chi}}^{3}(\ensuremath{-}\ensuremath{\omega};\ensuremath{\omega},0,0)],$ using a summation over states model dominated by the ground state, the ${1B}_{u}$ exciton, two strongly coupled ${A}_{g}$ states (${\mathrm{mA}}_{g}$ and ${\mathrm{kA}}_{g}$), and their most strongly coupled vibrations, using Frank-Condon overlap integrals. A distribution of conjugation lengths, which results in a distribution of excited state energies, was also incorporated into the model. The decomposition of the EA spectra due to the conjugation length distribution was then used to calculate the ${1B}_{u}$ exciton polarizability $(\ensuremath{\Delta}p)$ using first derivative analysis. For the longest conjugation lengths in our films, we found $\ensuremath{\Delta}p$ to be of order ${10}^{4}(\mathrm{\AA{}}{)}^{3}$ in luminescent polymers and ${10}^{3}{\mathrm{\AA{}}}^{3}$ in nonluminescent polymers, respectively, in good agreement with recent subnanosecond transient photoconductivity measurements. We also found that the Huang-Rhys parameter of the ${1B}_{u}$ exciton varies between 0.25 and 0.9, being in general smaller for the luminescent polymers. The consequent exciton relaxation energies were calculated to be of order 100 meV.