acid base - What is the Ka of OH- and Kb of H3O+?

What is the $K_\mathrm{a}$ of $\ce{OH^-}$ and $K_\mathrm{b}$ of $\ce{H_3O^+}$? Have these constants been determined?

Answer

For $\ce{O^2-}$, the $\mathrm{p}K_\mathrm{b}$ is approximately $-22$, so the $\mathrm{p}K_\mathrm{a}$ of hydroxide is about $36$.

sources: http://www.newworldencyclopedia.org/entry/Oxide and https://www.chem.tamu.edu/rgroup/hughbanks/courses/462/lecturenotes/class6-2.pdf

For hydronium, the reference Fred Senese cited

Protonated hydronium dication...

suggests that at acidities of Hammet acidity function $H_o = -25$ to $-28$, protonated hydronium can be present.