  We define the notion of hom-Batalin-Vilkovisky algebras and strong
differential hom-Gerstenhaber algebras as a special class of hom-Gerstenhaber
algebras and provide canonical examples associated to some well-known
hom-structures. Representations of a hom-Lie algebroid on a hom-bundle are
defined and a cohomology of a regular hom-Lie algebroid with coefficients in a
representation is studied. We discuss about relationship between these classes
of hom-Gerstenhaber algebras and geometric structures on a vector bundle. As an
application, we associate a homology to a regular hom-Lie algebroid and then
define a hom-Poisson homology associated to a hom-Poisson manifold.
