Following our first paper about high resolution spectroscopy of methyltrioxorhenium (MTO) [Stoeffler et al. PCCP, 13, 854, (2011)], the present study reports a deeper investigation of the ground state, and Re=O antisymmetric (nu_as) and symmetric (nu_s) stretching excited states of both CH3(187Re)O3 and CH3(185Re)O3 isotopologues, thanks to new devices implemented within our consortium. We carry out high resolution millimeter-wave (MMW) and infrared (IR) spectroscopy in room temperature absorption cells, in a pulsed supersonic jet and in a cryogenic buffer gas cell. This collection of sensitive spectrometers enables us to probe both levels of a vibrational transition in low and room temperature gaseous environments. We thus report a new series of measurements providing particularly accurate rotational and rovibrational data for such a large and heavy organometallic molecule that is solid at room temperature. The combination of the new MMW and IR data leads to an improvement of the rovibrational model of MTO: (i) rotational spectra are extended to the 150-300 GHz range and are analyzed to characterize the ground state rotational and hyperfine structure up to J = 43 and K = 41, resulting in the significant refinement of rotational, quartic and hyperfine parameters, as well as the determination of sextic parameters and a centrifugal distortion correction to the quadrupolar hyperfine constant, (ii) rovibrational data recorded at very different temperatures (between 6 and 300 K) in the 970-1015 cm-1 range, at resolutions down to 8 MHz and frequency accuracies as high as 30 MHz (using the buffer gas technique), are used in a first step to extract more precise excited-state rotational, Coriolis and quartic parameters as well as the ground-state centrifugal distortion parameter D_K of the 187Re isotopologue, which isn't accessible from rotational spectroscopy alone. In a second step, taking the hyperfine structure into account, the upper state rhenium atom quadrupole coupling constant eQq' is determined from the assignment of partially hyperfine-resolved CO2 laser absorption spectra of a skimmed molecular beam.