Efimov physics in two nuclear-spin sublevels of bosonic lithium is studied and it is shown that the positions and widths of recombination minima and Efimov resonances are identical for both states within the experimental errors, which indicate that the short-range physics is nuclear-spin independent. We also find that the Efimov features are universally related across Feshbach resonances. These results crucially depend on careful mapping between the scattering length and the applied magnetic field which we achieve by characterization of the two broad Feshbach resonances in the different states by means of rf-spectroscopy of weakly bound molecules. By fitting the binding energies numerically with a coupled channels calculation we precisely determine the absolute positions of the Feshbach resonances and the values of the singlet and triplet scattering lengths.