A comprehensive study of multi-nuclear (¹H, ²H, and ¹⁹F) magnetic resonance self-diffusion coefficients (D) and spin-lattice relaxation times (T₁) was done as functions of both temperature and pressure on selectively deuterated 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)amide (EMIM TFSA) ionic liquid isotopologues and related ionic liquids. While variable temperature studies provided useful insight, pressure dependent studies were more elucidating as discussed below.  First, stronger electric field gradients were indicated in the alkyl chain region compared to the imidazolium ring of EMIM TFSA as determined from variable temperature ²H T₁. Second and most significantly, variable pressure measurements of the EMIM and TFSA diffusion revealed independent motions for the cations and anions, with that of the TFSA anions being slowed much more by increasing pressure than for the EMIM cations.  Activation volumes were determined from the pressure dependent D data and values of 28.8 ± 2.5 cm³/mol and 14.6 ± 1.3 cm³/mol were obtained for TFSA and EMIM respectively.  Typically, smaller activation volumes support less restriction in motion. One possible explanation for this difference in behavior between EMIM and TFSA is that increasing pressure limits the conformational mobility of the TFSA. Third, variable pressure ²H T₁ data shows two T₁ regimes, for the MD₃ and D₂ isotopologues between 0.1-100 and 100-250 MPa respectively. These two regimes could represent dissimilar arrangements for the EMIM cation.  Activation volumes determined from the pressure dependent ²H T₁ data were 21 and 25 (0-100 MPa) and 11 and 12 (100-250 MPa) cm³/mol for the MD₃ and D₂ isotopologues, respectively. These and other details will be discussed.