Solid-state, natural-abundance Mo-95 NMR experiments of four different MoS2 materials have been performed on a magnet at B-0 = 19.6 T and on a new series-connected hybrid magnet at 35.2 T. Employing two different 2H-MoS2 (2H phase) materials, a "pseudo-amorphous" MoS2 nanomaterial and a MoS2 layer on an Al2O3 support of a hydrodesulfurization (HDS) catalyst, has enabled the introduction of solid-state Mo-95 NMR as an important analytical tool in the study of MoS2 nanomaterials. Mo-95 spin-lattice relaxation time (T-1) studies of 160- and 4-layer 2H-MoS2 samples at 19.6 and 35.2 T show their relaxation rate (1/T-1) increase in proportion to B-0(2). This is in accord with chemical shift anisotropy (CSA) relaxation, which is the dominant T-1(Mo-95) mechanism, with a large Mo-95 CSA of 1025 ppm determined for all four MoS2 nanomaterials. The dominant CSA mechanism suggests that the MoS2 band gap electrons are delocalized throughout the lattice-layer structures, thereby acting as a fast modulation source (omega(o)tau(c) << 1) for Mo-95 CSA in 2H-MoS2. A decrease in T-1(Mo-95) is observed for an increase in the B-0 field and for a decrease in the number of 2H-MoS2 layers. All four nanomaterials exhibit identical Mo-95 electric-field gradient (EFG) parameters. The T-1 results account for the several failures in retrieving the Mo-95 spectral EFG and CSA parameters for multilayer 2H-MoS2 samples in the pioneering solid-state Mo-95 NMR studies performed during the past 2 decades (1990-2010) because of the extremely long T-1(Mo-95) = similar to 200-250 s observed at a low B-0 (similar to 9.4 T) used at that time. Much shorter T-1(Mo-95) values are observed even at 19.6 T for the "pseudo-amorphous" and the HDS catalyst (MoS2-Al2O3 support) MoS2 nanomaterials. These allowed obtaining useful solid-state Mo-95 NMR spectra for these two samples at 19.6 T in a few to