  The charge ordered La$_{1/3}$Sr$_{2/3}$FeO$_{3-\delta}$ (LSFO) in bulk and
nanocrystalline forms are investigated using ac and dc magnetization,
M\"{o}ssbauer, and polarised neutron studies. A complex scenario of short range
charge and magnetic ordering is realized from the polarised neutron studies in
nanocrystalline specimen. This short range ordering does not involve any change
in spin state and modification in the charge disproportion between Fe$^{3+}$
and Fe$^{5+}$ compared to bulk counterpart as evident in the M\"{o}ssbauer
results. The refinement of magnetic diffraction peaks provides magnetic moments
of Fe$^{3+}$ and Fe$^{5+}$ are about 3.15$\mu_B$ and 1.57$\mu_B$ for bulk, and
2.7$\mu_B$ and 0.53$\mu_B$ for nanocrystalline specimen, respectively. The
destabilization of charge ordering leads to magnetic phase separation, giving
rise to the robust exchange bias (EB) effect. Strikingly, EB field at 5 K
attains a value as high as 4.4 kOe for average size $\sim$ 70 nm, which is zero
for the bulk counterpart. A strong frequency dependence of ac susceptibility
reveals cluster-glass like transition around $\sim$ 65 K, below which EB
appears. Overall results propose that finite size effect directs the complex
glassy magnetic behavior driven by unconventional short range charge and
magnetic ordering, and magnetic phase separation appears in nanocrystalline
LSFO.
