We present an optical spectroscopic study of a 90 per cent complete sample of nearby ULIRGs (z < 0.175) with optical Seyfert nuclei, with the aim of investigating the nature of the near-nuclear (r ≲ 3.5 kpc) warm gas outflows. A high proportion (94 per cent) of our sample show disturbed emission line kinematics in the form of broad (FWHM > 500 km s-1) and/or strongly blueshifted (ΔV < -150 km s-1) emission line components. This proportion is significantly higher than found in a comparison sample of nearby ultraluminous infrared galaxies (ULIRGs) that lack optical Seyfert nuclei (19 per cent). We also find evidence that the emission line kinematics of the Sy-ULIRGs are more highly disturbed than those of samples of non-ULIRG Seyferts and Palomar-Green quasars in the sense that, on average, their [O III] λλ5007, 4959 emission lines are broader and more asymmetric. The Sy-ULIRG sample encompasses a wide diversity of emission line profiles. In most individual objects, we are able to fit the profiles of all the emission lines of different ionization with a kinematic model derived from the strong [O III] λλ4959, 5007 lines, using between two and five Gaussian components. From these fits, we derive diagnostic line ratios that are used to investigate the ionization mechanisms for the different kinematic components. We show that, in general, the line ratios are consistent with gas of supersolar abundance photoionized by a combination of AGN and starburst activity, with an increasing contribution from the AGN with increasing FWHM of the individual kinematic components, and the AGN contribution dominating for the broadest components. However, shock ionization cannot be ruled out in some cases. Our derived upper limits on the mass outflows rates and kinetic powers of the emission line outflows show that they can be as energetically significant as the neutral and molecular outflows in ULIRGs - consistent with the requirements of the hydrodynamic simulations that include AGN feedback. However, the uncertainties are large, and more accurate estimates of the radii, densities and reddening of the outflows are required to put these results on a firmer footing.