Taub-NUT-AdS spaces are characterized by their nut parameter "n" which leads to a string-like singularity, or Misner String, in certain classes of solutions. To remove these singularities, one must identify time coordinates which in turn messes up the thermodynamics. We proposed a new pair of thermodynamics variables that leads to consistent thermodynamics, i.e., first law, Gibbs-Duhem and Smarr's relations are all satisfied. We apply this thermodynamics to Dyonic Taub-NUT-AdS solutions with spherical, flat and hyperbolic horizon geometries. We have considered canonical and mixed ensembles to study the phase structure of these solutions. This study showed some intriguing features, which were not reported before, among which the existence of two distinguished critical points with a continuous phase transition region in between. Furthermore, in flat and hyperbolic cases we have found a continuous phase transition that takes place only for low enough pressures and temperatures, in contrast with the Van der Waals behavior that characterizes charged AdS black holes!