Osmium tetroxide (OsO4) is a heavy tetrahedral molecule that constitutes a benchmark for quantum chemistry calculations. Its favorable spin statistics (due to the zero nuclear spin of oxygen atoms) is such that only A(1) and A(2) (T-d symmetry) rovibrational levels are allowed, leading to a dense but quite easily resolvable spectrum. We reinvestigate here the v(1)/v(3) stretching fundamental (940-980 cm(-1)) dyad region and perform new assignments and effective Hamiltonian parameter fits for the main isotopologue ((OsO4)-Os-192). We also investigate the v(2)/v(4) bending fundamental dyad (300-360 cm(-1)) for the first time and perform a preliminary analysis. New experimental data have been obtained at 0.001 cm(-1) resolution using an isotopically pure (OsO4)-Os-192 sample and the Synchrotron SOLEIL light source. Assignments and analyses were performed using SPVIEW and XTDS software, respectively. We provide precise effective Hamiltonian parameters, including the band centers for all of the fundamental levels and rotational constants for the ground state and for all four fundamental levels. We discuss isotopic shifts, estimate the equilibrium rotational constant B-e, and derive a precise value for the equilibrium bond length r(e)(Os-O) = 1.70919(16) angstrom. We also performed experiments to measure for the first time the IR integrated intensities for the v(2)/v(4) bending fundamental dyad. These new data are compared to current ab initio predictions.