Densities, rho(123), and speeds of sound, u(123), of 1-ethyl-3-methylimidazolium tetrafluoroborate (1) + 2-methylaniline (2) + pyridine or alpha-, beta-, or gamma-picoline (3) ternary mixtures have been measured over the entire range of composition at 293.15 K, 298.15 K, 303.15 K, and 308.15 K using density and speed of sound analyzer (Anton Paar DSA 5000). The heat capacity, C-p, of pure liquids pyridine and alpha-, beta-, and gamma-picoline have also been measured at 293.15 K, 298.15 K, 303.15 K, and 308.15 K using differential scanning calorimeter. The measured data have been employed to determine excess molar volumes, V-123(E) and excess isentropic compressibilities,(kappa(E)(S))(123). The V-123(E) and(kappa(E)(S))(123) data have been fitted to Redlich-Kister equation to calculate ternary adjustable parameters and standard deviations. The thermodynamic properties of the ternary mixtures have been analyzed in terms of Graph (which deals with the topology of the constituent of mixtures) and Prigogine-Flory-Patterson (PFP) theories. It has been observed that Graph theory describes well V-123(E) and (kappa(E)(S))(123) data of the studied ternary ionic liquid mixtures. However, PFP theory correctly predicts the sign of V-123(E) and (kappa(E)(S))(123) data of the studied mixtures.