  The effect of the spin-orbit coupling on the ground state properties of the
square-lattice three-band Hubbard model with a single electron per site is
studied by a generalized Hartree-Fock approximation. We calculate the full
phase diagram and show that there appear additional orbital-entangled phases
brought about by competition of various exchange channels or by the spin-orbit
coupling in addition to conventional states stabilized by the Kugel-Khomskii
mechanism. One of these phases previously proposed to explain magnetic
properties of Sr$_2$VO$_4$ is characterized by vanishing dipolar magnetic
moments and antiferro-octupolar ordering. We calculated microscopic parameters
for this material and demonstrate that it is located near a phase boundary of
two orbital-entangled and two conventional antiferromagnetic ferro-orbital
states.
