Positron annihilation lifetime spectroscopy (PALS) was used to study a series of ionic liquids (ILs) with the 1-butyl-3-methylimidazolium cation ([C4MIM](+)) but different anions [Cl](-), [BF4](-), [PF6](-), [OTf](-), [NTf2](-), and [B(hfip)4](-) with increasing anion volumes. Changes of the ortho-positronium (o-Ps) lifetime parameters with temperature were observed for crystalline and amorphous (glass, supercooled, and normal liquid) states. Evidence for distinct phase transitions, e.g. melting, crystallization and solid-solid transitions, was observed in several PALS experiments. The o-Ps mean lifetime τ3 showed smaller values in the crystalline phase due to dense packing of the material compared to the amorphous phase. The o-Ps lifetime intensity I3 in the liquid state is clearly smaller than in the crystallized state. This behaviour can be attributed to a solvation of e(+) by the anions, which reduces the Ps formation probability in the normal and supercooled liquid. These phenomena were observed for the first time when applying the PALS technique to ionic liquids by us in one preliminary and in this work. Four of the ionic liquids investigated in this work ([BF4](-), [NTf2](-), [PF6](-) and [Cl](-) ILs) exhibit supercooled phases. The specific hole densities and occupied volumes of those ILs were obtained by comparing the local free volume with the specific volume from pressure-volume-temperature (PVT) experiments. From the o-Ps lifetime, the mean size vh of free volume holes of the four samples was calculated and compared with that calculated according to Fürth's hole theory. The hole volumes from both methods agree well. From the Cohen-Turnbull fitting of viscosity and conductivity against PALS/PVT results, the influence of the free volume on molecular transport properties was investigated.