We report the growth of high-quality epitaxial Sr2FeMoO6 (SFMO) thin films on various unconventional oxide substrates, such as TbScO3, DyScO3, and Sr2Al0.3Ga0.7TaO6 (SAGT) as well as on the most commonly used one, SrTiO3 (STO), by pulsed laser deposition. The films were found to contain a foreign nano-scale phase coherently embedded inside the SFMO film matrix. Through energy dispersive X-ray spectroscopy and scanning transmission electron microscopy, we identified the foreign phase to be Sr2−xFe1+yMo1−yO6, an off-stoichiometric derivative of the SFMO compound with Fe rich content (y ≈ 0.6) and a fairly identical crystal structure to SFMO. The films on STO and SAGT exhibited very good magnetic properties with high Curie temperature values. All the samples have fairly good conducting behavior albeit the presence of a foreign phase. Despite the relatively large number of items of the foreign phase, there is no significant deterioration in the properties of the SFMO films. We discuss in detail how magneto-transport properties are affected by the foreign phase.