The development of in-plane orbital ordering with oxygen deficiency is investigated in epitaxially strained thin films of La_0.7Sr_0.3MnO_{3- δ} grown under in-plane tensile strain on SrTiO₃ substrates. The orbital character of 3d states is directly probed by linear dichroism in X-ray absorption spectroscopy at the Mn L_{2, 3} and O K edges. The electrical transport measurements show a rapid decrease of the metal-insulator transition temperature and an increase of the polaronic activation energy when reducing the oxygen content. The diffraction measurements show a contraction of the average out-of-plane lattice parameter due to an enhancement of the regular distribution of the Mn³⁺ distorted octahedra in oxygen-deficient films. We show that the oxygen deficiency and the in-plane tensile strain cooperate to stabilize the in-plane orbital occupation: the oxygen deficiency is responsible for the increased number of Jahn-Teller distorted octahedra and the in-plane tensile strain drives the arrangement of such octahedra, favoring the in-plane confinement of the e_g orbitals. Linear dichroism in X-ray absorption also demonstrates that the Mn 3d/O 2p hybridization changes little with the oxygen content, thus confirming that the in-plane orbital ordering is the main factor influencing the transport properties.