In the potential event of a clad breach in a Sodium-cooled Fast Reactor (SFR), the sodium metallic coolant could come into contact with the (U,Pu,Np)$O2$ nuclear fuel. The reaction products are numerous, but there is little knowledge of their structural and thermodynamic properties. Under the oxygen potential conditions of the reactor, pentavalent $Na3AnO4$ (An=U,Pu,Np) is expected to form, but its structure was the subject of controversy until now. We showed that $\alpha -Na3UO4$ adopts a monoclinic symmetry in space group $P2/c$. Neutron diffraction combined with X-ray Absorption Near Edge Structure (XANES) spectroscopy at the U-M$4$ edge also revealed that this phase could accommodate excess sodium on the uranium site, with subsequent charge compensation of the uranium cation from U(V) to U(VI), which was not previously foreseen. The corresponding mixed valence state composition is written $Na3(U1-x,Nax)O4$ with 0<$x$<0.16(2). To complete the data on the Na-U-O system, the thermodynamic functions of $Na2U2O7$ and $Na4UO5$ were evaluated using Knudsen effusion mass spectrometry (KEMS) and thermal-relaxation calorimetry. In addition, the oxygen content required at 900 K within liquid sodium to form pentavalent $Na3UO4$ and hexavalent $Na4UO5$ were calculated to be 0.7 and 1.5 wppm, respectively, which are levels typically encountered in SFRs. A thermodynamic model for the Np-O system was then developed using the CALPHAD method. This is particularly relevant since it is envisaged to incorporate minor actinides into the fuel to minimize the nuclear waste inventory. The poorly known structures of the Na- Np-O and Na-Pu-O phases diagrams, i.e., tetravalent $Na2AnO3$ (An=Np,Pu), pentavalent $Na3AnO4$, hexavalent $Na4AnO5$ and $\alpha -Na2NpO4$, and heptavalent $Na5AnO6$, were also re-fined by the Rietveld method. The structures of $Na3NpO4$ and $Na3PuO4$ were determined ab initio from powder X-ray diffraction data, and found to be orthorhombic in the space group $Fmmm$. The valence states of the neptunium cations were confirmed from the isomer shift values of their Mössbauer spectra. Having established the charge states without ambiguity, XANES spectra were collected at the $Np-L3$ and $Pu-L3$ edges to serve as reference data for An(V), An(VI), and An(VII) oxide phases in the solid state. Finally, KEMS studies of $\alpha -Na2NpO4$ showed very promising results for the determination of the enthalpies of formation of the sodium neptunates and plutonates, for which there is almost no data available. The heat capacities and entropies at 298.15 K of $\alpha -Na2NpO4$, $Na4NpO5$, $Na5NpO6$, and $Na5PuO6$ were also determined. Comparing their Gibbs energy values, the sodium neptunates were found to be slightly more stable than their isostructural uranium analogues.