Which are stronger intermolecular forces: ionic bonds or hydrogen bonds?
Hydrogen bonds are the strongest intermolecular forces. Stronger than van der Waals' forces, namely (ordained by strength):


Permanent dipole - permanent dipole (Keesom's Force);
Permanent dipole - induced dipole (Debye force);
induced dipole - induced dipole (London's dispersion force);


Strong hydrogen bonds are created by the FONs (fluorine, Oxygen and Nitrogen), which are very electronegatives, what produces a strong attraction between one them and hydrogen (which is less electronegative). As example of this interaction we can cite the water, that's a polar molecule in a "V" shape, take a look at the figure below. 

Then, the both hydrogens yields a $\delta^{+}$ that's attracted by the Oxygen (very strong electronegative, the $\delta^{-}$ side) of the another water molecule, yielding the hydrogen bonds, take a look at the figure below.