We study instabilities of single-species fermionic atoms in the
p-orbital bands in two-dimensional optical lattices at noninteger filling against interactions. Charge density wave and orbital density wave orders with stripe or checkerboard patterns are found for attractive and repulsive interactions, respectively. The superfluid phase, usually expected of attractively interacting fermions, is strongly suppressed. We also use field theory to analyze the possible phase transitions from orbital stripe order to liquid-crystal phases and obtain the phase diagram. The condition of nearly-perfect Fermi-surface nesting, which is key to the above results, is shown robustly independent of fermion fillings in such
p-orbital systems, and the $(2{k}_{F},\ifmmode\pm\else\textpm\fi{}2{k}_{F})$ momentum of density wave oscillation is highly tunable. Such remarkable features show the promise of making those exotic orbital phases, which are of broad interest in condensed-matter physics, experimentally realizable with optical lattice gases.