  We analyse van der Waals interactions between a pair of dielectrically
anisotropic plane-layered media interacting across a dielectrically isotropic
solvent medium. We develop a general formalism based on transfer matrices to
investigate the van der Waals torque and force in the limit of weak
birefringence and dielectric matching between the ordinary axes of the
anisotropic layers and the solvent. We apply this formalism to study the
following systems: (i) a pair of single anisotropic layers, (ii) a single
anisotropic layer interacting with a multilayered slab consisting of
alternating anisotropic and isotropic layers, and (iii) a pair of multilayered
slabs each consisting of alternating anisotropic and isotropic layers, looking
at the cases where the optic axes lie parallel and/or perpendicular to the
plane of the layers. For the first case, the optic axes of the oppositely
facing anisotropic layers of the two interacting slabs generally possess an
angular mismatch, and within each multilayered slab the optic axes may either
be the same, or undergo constant angular increments across the anisotropic
layers. In particular, we examine how the behaviors of the van der Waals torque
and force can be "tuned" by adjusting the layer thicknesses, the relative
angular increment within each slab, and the angular mismatch between the slabs.
