Translational diffusion coefficients of diphenylcyclopropenone (DPCP), diphenylacetylene (DPA), and carbon monoxide (CO) in 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide ([BMIm][NTf2]) and 1-ethyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide ([EMIm][NTf2]) were determined by the transient grating (TG) spectroscopy under pressure from 0.1 to 200 MPa at 298 K and from 298 to 373 K under 0.1 MPa. Diffusion coefficients of these molecules at high temperatures in tributylmethylphosphonium bis(trifluoromethanesulfonyl)imide ([P-4441][NTf2]), and tetraoctylphosphonium bis(trifluoromethanesulfonyl)imide ([P-8888][NTf2]), and also in the mixtures of [BMIm][NTf2], N-methyl-N-propylpiperidinium bis(trifluoromethanesulfonyl)imide ([Pp(13)][NTf2]), and trihexyltetradecylphosphonium bis(trifluoromethanesulfonyl)imide ([P-66614][NTf2]) with ethanol or chloroform have been determined. Diffusion coefficients except in ILs of phosphonium cations were well scaled by the power law of T/eta, i.e., (T/eta)(P), where T and eta are the absolute temperature and the viscosity, irrespective of the solvent species, pressure and temperature, and the compositions of mixtures. The values of the exponent P were smaller for the smaller size of the molecules. On the other hand, the diffusion coefficients in ILs of phosphonium cations with longer alkyl chains were larger than the values expected from the correlation obtained by other ILs and conventional liquids. The deviation becomes larger with increasing the number of carbon atoms of alkyl-chain of cation, and with decreasing the molecular size of diffusing molecules. The molecular size dependence of the diffusion coefficient was correlated by the ratio of the volume of the solute to that of the solvent as demonstrated by the preceding work (Kaintz et al., J. Phys. Chem. B 2013, 117, 11697). Diffusion coefficients have been well correlated with the power laws of both T/eta and the relative volume of the solute to the solvent.