The structural and thermodynamic properties of model molecular fluids of linear aggregates of Lennard-Jones sites was investigated using molecular dynamics simulation, reference interaction site model (RISM), and hypernetted-chain theory (HNC). This paper presents molecules of two, three, and five sites, and of aspect ratios 1.5, 2, and 3, respectively. The emphasis is given here to the numerical solution of HNC closure for molecular fluids with nonspherical soft interactions. Appropriate expressions for excess internal energy and virial pressure are derived. It is shown that the excess internal energies as given by both theories are in relatively good agreement with the simulations, mainly in the low-medium density and high temperature limits, while for the virial equation of state RISM theory is generally better than HNC for the high densities. The density correlation functions as predicted by the HNC theory are in overall better agreement with the simulation data, for all aspect ratios, whereas RISM theory results show some marked discrepancies for large aspect ratios.