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We explore the implications of our optical spectroscopic survey of 3CR radio sources with z<0.3 for the unified model (UM) for radio-loud AGN, focusing on objects with a ``edge-brightened'' (FR II) radio morphology. The sample contains 33 high ionization galaxies (HIGs) and 18 broad line objects (BLOs). According to the UM, HIGs, the narrow line sources, are the nuclearly obscured counterparts of BLOs. The fraction of HIGs indicates a covering factor of the circumnuclear matter of 65% that corresponds, adopting a torus geometry, to an opening angle of 50°±5. No dependence on redshift and luminosity on the torus opening angle emerges. We also consider the implications for a ``clumpy'' torus. The distributions of total radio luminosity of HIGs and BLOs are not statistically distinguishable, as expected from the UM. Conversely, BLOs have a radio core dominance, R, more than ten times larger with respect to HIGs, as expected in case of Doppler boosting when the jets in BLOs are preferentially oriented closer to the line of sight than in HIGs. Modeling the R distributions leads to an estimate of the jet bulk Lorentz factor of Γ∼3-5. The test of the UM based on the radio source size is not conclusive due to the limited number of objects and because the size distribution is dominated by the intrinsic scatter rather than by projection effects. The [OII] line luminosities in HIGs and BLOs are similar but the [OIII] and [OI] lines are higher in BLOs by a factor of ∼2. We ascribe this effect to the presence of a line emitting region located within the walls of the obscuring torus, visible in BLOs but obscured in HIGs, with a density higher than the [OII] critical density. We find evidence that BLOs have broader [OI] and [OIII] lines than HIGs of similar [OII] width, as expected in the presence of high density gas in the proximity of the central black hole. In conclusion, the radio and narrow line region (NLR) properties of HIGs and BLOs are consistent with the UM predictions when the partial obscuration of the NLR is taken into account. We also explored the radio properties of 21 3CR low ionization galaxies with a FR II radio morphology at z<0.3. We find evidence that they cannot be part of the model that unifies HIGs and BLOs, but they are instead intrinsically different source, still reproduced by a randomly oriented population.