  We study nuclear effects in the structure function F_3 which describes the
parity violating part of the charged-current neuitrino nucleon deep inelastic
scattering. Starting from a covariant approach we derive a factorized
expression for the nuclear structure function in terms of nuclear spectral
function and off-shell nucleon structure functions valid for arbitrary momentum
transfer Q and in the limit of weak nuclear binding, i.e. when a nucleus can be
treated as a non-relativistic system. We develop a systematic expansion of
nuclear structure functions in terms of Q^{-2} series caused by nuclear effects
("nuclear twist" series). Basing on this expansion we calculate nuclear
corrections to the Gross-Llewellyn-Smith sum rule as well as to higher moments
of F_3. We show that corrections to the GLS sum rule due to nuclear effects
cancel out in the Bjorken limit and calculate the corresponding Q^{-2}
correction. Special attention is payed to the discussion of the off-shell
effects in the structure functions. A sizable impact of these effects both on
Q^2- and x-dependence of nuclear structure functions is found.
