General methods are developed for evaluating Mayer cluster diagrams for systems of molecules with orientation-dependent forces. These methods are particularly useful for obtaining chain and ring contributions. Simplification occurs for ordinary two-body forces in the absence of external fields because of invariance under rotation of the two-body complex as a whole. Using these methods we adapt Mayer's rearrangement procedure to calculate the cluster expansion of the potential of the average force between two ionic or dipolar solute molecules that are immersed and fixed in a gas of dipolar molecules. The comparison of this potential with the corresponding macroscopic quantity leads to a cluster expansion for the dielectric constant of the dipolar gas.