  We study exotic superconducting states in SrTiO$_3$ heterostructures on the
basis of the three-orbital model, which reproduces the band structure of
two-dimensional electron gases. We show various
Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states induced by the broken inversion
symmetry and orbital degree of freedom. In particular, a novel
orbital-dependent FFLO state is stabilized in a magnetic field along the
[110]-axis. The field angle dependence of the FFLO state is clarified on the
basis of the spin and orbital texture in the momentum space. It is shown that
the orbital degree of freedom in Cooper pairs gives rise to in-plane anisotropy
of the critical magnetic field. The carrier density dependence of the
superconducting state is also discussed.
