OsO4 is sp3 hybridised.
The oxidation state of osmium in this compound is +8. Hence it's d-orbitals are emptied in making the bonds to the oxygen atoms (oxygen is more electronegative and "hogs" the electrons from osmiums d-orbitals to form resonance stabilized double bonds). With the d-orbitals unoccupied, osmium can assume a geometry characteristic of a hybridization between its filled s and p orbitals.
This isn't the only oxide that forms an sp3 configuration with metals even though the metal has d-orbitals. The structures for permanganate ion (MnO4-, with Mn at +7), manganate ion ( MnO42-, with Mn at +6), and Cromate ion (CrO42-, with Cr at +6) give the same geometry, and if you notice these metals are a few rows up the periodic table and appear just to the left of osmium's group.