  This is the sixth paper presenting the results of the MUse RAdio Loud
Emission line Snapshot survey (MURALES). We observed 37 radio sources from the
3C sample with z<0.3 and declination <20 degrees with the MUSE optical integral
field spectrograph at the VLT. We here 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 10 FRIs is, in
most cases, confined to within <4 kpc, while large-scale (>4 kpc) ionized gas
is seen in all but two of the 26 FRIIs. 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 1) the large-scale ionized gas
structures show a tendency to be oriented at large angles from the radio axis,
and 2) the gas on a scale of a few kpc from the nucleus often shows ordered
rotation with a kinematical axis forming a median angle of 65 degrees 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" 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.
