  This is a paper in a series systematically to study toroidal vertex algebras.
Previously, a theory of toroidal vertex algebras and modules was developed and
toroidal vertex algebras were explicitly associated to toroidal Lie algebras.
In this paper, we study twisted modules for toroidal vertex algebras. More
specifically, we introduce a notion of twisted module for a general toroidal
vertex algebra with a finite order automorphism and we give a general
construction of toroidal vertex algebras and twisted modules. We then use this
construction to establish a natural association of toroidal vertex algebras and
twisted modules to twisted toroidal Lie algebras. This together with some other
known results implies that almost all extended affine Lie algebras can be
associated to toroidal vertex algebras.
