We report in this article a comprehensive investigation of the viscoelastic behavior of different natural colloidal clay minerals in aqueous solution. Rheological experiments were carried out under both dynamic and steady-state conditions, allowing us to derive the elasticity and yield stress. Both parameters can be renormalized for all sizes, ionic strength, and type of clay using in a first approach only the volume of the particles. However, applying such a treatment to various clays of similar shapes and sizes yields differences that can be linked to the repulsion strength and charge location in the swelling clays. The stronger the repulsive interactions, the better the orientation of clay particles in flows. In addition, a master linear relationship between the elasticity and yield stress whose value corresponds to a critical deformation of 0.1 was evidenced. Such a relationship may be general for any colloidal suspension of anisometric particles as revealed by the analysis of various experimental data obtained on either disk-shaped or lath- and rod-shaped particles. The particle size dependence of the sol gel transition was also investigated in detail. To understand why suspensions of larger particles gel at a higher volume fraction, we propose a very simplified view based on the statistical hydrodynamic trapping of a particle by an another one in its neighborhood upon translation and during a short period of time. We show that the key parameter describing this hydrodynamic trapping varies as the cube of the average diameter and captures most features of the sol gel transition. Finally, we pointed out that in the high shear limit the suspension viscosity is still closely related to electrostatic interactions and follows the same trends as the viscoelastic properties.