This is the sixth paper presenting the results of the MUse RAdio Loud Emission line Snapshot survey. We observed 37 radio sources from the 3C sample with z < 0.3 and a declination < 20° with the Multi Unit Spectroscopic Explorer optical integral field spectrograph at the Very Large Telescope. Here, we focus on the properties of the extended emission line regions (EELRs) that can be studied with unprecedented detail thanks to the depth of these observations. Line emission in the ten FR Is is, in most cases, confined to within ≲4kpc, while large-scale (≳4 kpc) ionized gas is seen in all but two of the 26 FR IIs. It usually takes the form of elongated or filamentary structures, typically extending between 10 and 30 kpc, but also reaching distances of ∼80 kpc. We find that the large-scale ionized gas structures show a tendency to be oriented at large angles from the radio axis, and that the gas on a scale of a few kiloparsecs from the nucleus often shows ordered rotation with a kinematical axis forming a median angle of 65° with the radio axis. We also discuss the velocity field and ionization properties of the EELRs. The observed emission line structures appear to be associated with gaseous "superdisks" that formed after a gas-rich merger. The different properties of the EELR can be explained with a combination of the source evolutionary state and the orientation of the superdisk with respect to the radio axis. The general alignment between the superdisks and radio axis might be produced by stable and coherent accretion maintained over long timescales.