We present an atomistic pseudopotential study of the electronic and optical properties of InAs quantum rods as a function of increasing length-to-diameter ratio. We show that, as the aspect ratio increases, energy levels cross in both conduction and valence bands, reflecting their different dependence on confinement along a specific direction. Unlike in CdSe and InP quantum rods, however, the position of the crossover between highest occupied molecular orbitals with different symmetries is found to be size-dependent and the value of the aspect ratio at the crossing to increase with the rod diameter. We find that the level crossings at the top of the valence band are crucial to explain the evolution with elongation of all optical properties in these systems. Their transformation from zero- to quasi-one-dimensional structures is characterized by a common monotonic behavior of band gap, Stokes shift, degree of linear polarization, and radiative lifetime, closely linked to the variation with aspect ratio of the electronic structure of the nanocrystal valence band edge. This characteristic feature was not observed in elongated CdSe structures, whose optical properties exhibited instead a distinctive non-monotonic evolution with length, with a turning point associated with a crossover at the top of the valence band, similar to that found here between states with σ and π symmetries.