  We construct vertex operator representations for the full (N+1)-toroidal Lie
algebra g. We associate with g a toroidal vertex operator algebra, which is a
tensor product of an affine VOA, a sub-VOA of a hyperbolic lattice VOA, affine
sl(N) VOA and a twisted Heisenberg-Virasoro VOA. The modules for the toroidal
VOA are also modules for the toroidal Lie algebra g. We also construct
irreducible modules for an important subalgebra gdiv of the toroidal Lie
algebra that corresponds to the divergence free vector fields. This subalgebra
carries a non-degenerate invariant bilinear form. The VOA that controls the
representation theory of gdiv is a tensor product of an affine VOA Vaff(c) at
level c, a sub-VOA of a hyperbolic lattice VOA, affine sl(N) VOA and a Virasoro
VOA at level cvir with the following condition on the central charges: 2(N+1) +
rank Vaff(c) + cvir = 26.
