Electrostatic streaming instabilities have been proposed as the generation mechanism for the electrostatic solitary waves observed in various space plasma environments. Past studies on the subject have been mostly based on the kinetic theory and particle simulations. In this paper, we extend our recent study based on one-dimensional fluid theory and particle simulations to two-dimensional regimes for both bi-streaming and bump-on-tail streaming instabilities in electron-ion plasmas. Both linear fluid theory and kinetic simulations show that for bi-streaming instability, the oblique unstable modes tend to be suppressed by the increasing background magnetic field, while for bump-on-tail instability, the growth rates of unstable oblique modes are increased with increasing background magnetic field. For both instabilities, the fluid theory gives rise to the linear growth rates and the wavelengths of unstable modes in good agreement with those obtained from the kinetic simulations. For unmagnetized and weakly magnetized systems, the formed electrostatic structures tend to diminish after the long evolution, while for relatively stronger magnetic field cases, the solitary waves may merge and evolve to steady one-dimensional structures. Comparisons between one and two-dimensional results are made and the effects of the ion-to-electron mass ratio are also examined based on the fluid theory and kinetic simulations. The study concludes that the fluid theory plays crucial seeding roles in the kinetic evolution of electrostatic streaming instabilities.