  We present a comprehensive study of a one-dimensional two-orbital model at
and below quarter-filling that realizes a number of unconventional phases. In
particular, we find an excitonic density wave in which excitons quasi-condense
with finite center of mass momentum and an order parameter that changes phase
with wave-vector $Q$. In this phase, excitons behave as hard-core bosons
without charge order. In addition, excitons can pair to form bi-excitons in a
state that is close to a charge density-wave instability. When pairing
dominates over the inter-orbital repulsion, we encounter a regime in which one
orbital is metallic, while the other forms a spin gapped superconductor, a
genuine orbital selective paired state. All these results are supported by
both, analytical and numerical calculations. By assuming a quasi-classical
approximation, we solve the three-body hole-electron-spinon problem and show
that excitons are held together by forming a bound state with spinons. In order
to preserve the antiferromagnetic background, excitons acquire a dispersion
that has a minimum away from $k=0$. The full characterization of the different
phases is obtained by means of extensive density matrix renormalization group
calculations.
