Hydrodynamic studies have been performed of accretion onto 1.00 M., 1.25 M., and 1.35 M. oxygen-neon-magnesium (ONeMg) white dwarfs at a rate of 10(17) g s(-1). The material from the companion star is expected to be of solar composition but is assumed to be mixed with material from the underlying white dwarf during accretion, such that the accumulating envelope material is enriched in oxygen, neon, and magnesium to fifty percent by mass. A new, expanded nuclear reaction network, utilizing up-to-date reaction rates and including 78 nuclei up to Ca-40, has been used in combination with the hydrodynamics for the first time in this study. We again find that the outbursts become more violent as the assumed white dwarf mass is increased. Burning temperatures, nuclear energy generation rates, and ejecta velocities all increase significantly with mass. A peak burning temperature of 356 x 10(6) K is reached in the 1.35 M. sequence, allowing significant nucleosynthesis of intermediate-mass elements to occur. We find that as we increase the white dwarf mass, the abundance of Al-26 decreases (by about a factor of 3 for our range of white dwarf masses), and the abundances of Na-22 and the majority of nuclei in the Si-Ca range increase significantly (by 2 orders of magnitude or greater). Our simulations indicate that nova outbursts which occur on ONeMg white dwarfs having a mass of 1.25 M. or greater produce sufficient amounts of Na-22 such that gamma-rays from the decay of Na-22 should be detectable with the Compton Gamma Ray Observatory, if the nova is nearby (D similar to 1 kpc). Our simulations also confirm that nova outbursts occurring on ONeMg white dwarfs are an important source of Al-26 nuclei in the Galaxy. We further examine whether such outbursts can fully account for the reported similar to 3 M. of Al-26 needed to explain the Galactic 1.809 MeV gamma-ray line emissions. We estimate that a minimum mass of 1.2 M. for ONeMg white dwarfs in binaries is needed in order for nova outbursts to be able to produce the observed similar to 3 M. of Al-26 over the mean lifetime of this nucleus. However, this estimate is based on the particular initial conditions we have chosen for the sequence of models presented in this paper, and on the assumption that the production of cataclysmic variables with ONeMg white dwarfs is not significantly less than that assumed for CO white dwarfs in the same mass range.