Room temperature ionic liquids differ from molten salts in many ways, our work concentrates on two distinguishing features. These are large cation-anion size disparities and at least one ionic species where the center of mass and the center of charge do not coincide. In earlier work, we examined the influences of these features in isolation on simple spherical models. This paper extends this work to ionic liquid models where both features are present, and where the characteristic distance sigma(+-) (') determining the strength of the Coulombic attractions is unconstrained. We consider the interplay among these molecular features and elucidate their relative importance to the behavior of ionic liquids. Particular attention is focused on the transport properties. We find that size disparity, charge location, and sigma(+-) (') can all have large (often competing) effects. In our models, size disparity and small charge displacements lead to weakly bound, directional ion pairs, and the resulting asymmetric ion-counterion distribution gives rise to increased diffusion coefficients, consequently lower viscosity, and increased conductivity. These observations are analogous to effects reported in the literature, and we see similarities between the directional ion pairs in our models and directional cation-anion pairing through weak hydrogen bonding in room temperature ionic liquids. In our models, large charge displacements lead to strongly bound, long-lived, directional ion pairs, and in this regime the trends noted above are reversed, increased viscosities, and decreased conductivities are observed. Recently, creating more strongly hydrogen bonded, directional ion pairs has been put forward as possible means of achieving larger viscosity reductions. The trend reversal that we observe suggests that this might not work in practice.