Systems of platelet-shaped nanostacks of the synthetic clay Na-fluorohectorite, suspended in saline solutions of various salt concentrations, exhibit a rich phase behavior with up to four phases coexisting in a single sample tube. They are studied here using small-angle x-ray scattering: the anisotropy of the obtained images is quantified, and, together with x-ray absorption measurements, this provides a precise determination of the phase boundaries, as well as a measure of the orientational ordering of the clay colloids in the various gel phases. The coexistence of different phases results from a sedimentation-induced vertical gradient in particle fraction. Quantitative relation of the vertical coordinate to the clay particle fraction in these samples allows determination of a phase diagram for these Na-fluorohectorite systems, as a function of the particle fraction and salt concentration.