Do the compounds NaₓIrO₂ and NaOsO₂ exist?
For $\ce{Na_{x}IrO2}$ the current answer seems to be "no" it has not been made but it is discussed in the literature theoretically.

From Kitaev-Heisenberg models for iridates on the triangular, hyperkagome, kagome, fcc, and pyrochlore lattices:


  However, no triangular lattice iridate with the relevant edge sharing octahedra structure is currently available; a compound of the
  type NaxIrO2 may or may not turn out to be stabilized.


and in Chiral spin liquid and topological superconductivity in the undoped and doped
triangular Kitaev-Heisenberg model: 


  In addition, a class of ABO2 (where A and B are alkali and transition metal ions, respectively) type transition metal compounds and the possible material NaxIrO2 may be potential candidates for realizing the triangular Kitaev-Heisenberg model.


(But that's your paper isn't it? I don't have any information beyond what you already know, so really this is a useless answer.)