We present results for organic liquids modeled as linear rods with an embedded point dipole shifted from the geometrical center. Previously, we have obtained results for the vapor-liquid equilibrium (VLE) of similar systems with centered point dipoles. Our results included both models and applications to real systems. Results presented here are based on a previous work ( Phys. Rev. E 2003, 68, 021201) on the structural properties of these systems where relevant results about the appearance of dimers were found. Now, we have also performed systematic simulations on these systems to calculate the VLE of models with different aspect ratios, dipole shifts, and dipole strengths using the Gibbs ensemble Monte Carlo (GEMC) to calculate equilibrium densities and vapor pressure at each temperature. The applications considered here include some important substances such as 1-amines, acetonitrile, and 1-alcohols whose intermolecular parameters were fitted from our model simulations. Furthermore, we have used quantum chemistry calculations to obtain a reliable charge distribution, and we have applied our model to predict the vapor pressure of alpha,omega-diols where experimental results are rather scarce. Our results show a general improvement of the agreement between experiment and models compared to centered dipole models previously used. Results for amines are particularly remarkable.