Oxygen packaging in transition metal oxides determines the metal-oxygen hybridization and electronic occupation at metal orbitals. Strontium vanadate (SrVO$_3$), having a single electron in a $3d$ orbital, is thought to be the simplest example of strongly correlated metallic oxides. Here, we determine the effects of epitaxial strain on the electronic properties of SrVO$_3$ thin films, where the metal-oxide sublattice is corner-connected. Using x-ray absorption and x-ray linear dichroism at the V $L_{2,3}$ and O $K$-edges, it is observed that tensile or compressive epitaxial strain change the hierarchy of orbitals within the $t_{2g}$ and $e_g$ manifolds. Data show a remarkable $2p-3d$ hybridization, as well as a strain-induced reordering of the V $3d$($t_{2g}$, $e_g$) orbitals. The latter is itself accompanied by a consequent change of hybridization that modulates the hybrid $pi^*$ and $sigma^*$ orbitals and the carrier population at the metal ions, challenging a rigid band picture.
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