We present a multiwavelength study of the OH Megamaser galaxy (OHMG) IRAS16399-0937, based on new HST/ACS F814W and H$alpha$+[NII] images and archive data from HST, 2MASS, Spitzer, Herschel and the VLA. This system has a double nucleus, whose northern (IRAS16399N) and southern (IRAS16399S) components have a projected separation of $sim$ 6 (3.4 kpc) and have previously been identified based on optical spectra as a Low Ionization Nuclear Emission Line Region (LINER) and starburst nucleus, respectively. The nuclei are embedded in a tidally distorted common envelope, in which star formation is mostly heavily obscured. The infrared spectrum is dominated by strong polycyclic aromatic hydrocarbon (PAH), but deep silicate and molecular absorption features are also present, and are strongest in the IRAS16399N nucleus. The 0.435 - 500$mu$m SED was fitted with a model including stellar, ISM and AGN torus components using our new MCMC code, clumpyDREAM. The results indicate that the IRAS16399N contains an AGN (L$_{bol} sim 10^{44}$ ergs/s) deeply embedded in a quasi-spherical distribution of optically-thick clumps with a covering fraction $approx1$. We suggest that these clumps are the source of the OHM emission in IRAS16399-0937. The high torus covering fraction precludes AGN-photoionization as the origin of the LINER spectrum, however, the spectrum is consistent with shocks (v $sim100-200$ km s$^{-1}$). We infer that the $sim10^8$ M$_{odot}$ black-hole in IRAS16399N is accreting at a small fraction ($sim1$%) of its Eddington rate. The low accretion-rate and modest nuclear SFRs suggest that while the gas-rich major merger forming the IRAS16399-0937 system has triggered widespread star formation, the massive gas inflows expected from merger simulations have not yet fully developed.