Why are bonding interactions so much stronger than all the other types of interactions like dipole-dipole, London dispersion, hydrogen bond etc. even though they are all of electromagnetic origin?
Bonding interactions effectively share electrons. In a gedankenexperiment, you can think of two isolated species with many unpaired electrons coming together, bonding and forming a species with less unpaired electrons. The exact nature of bonds is slightly different, involves quantum mechanics and orbitals, but the end of the story is that the electrons are in a less energetic state after bonding than before it. The energy gained by this process is rather significant, typically hundreds of kilojoules per mole.
These bonds that are created typically generate a molecule or some type of network solid (ionic, metallic or covalent). If you have generated a molecule, then you can rather easily separate a single molecule from all the surrounding molecules by physical methods such as high vacuum. It is not possible, however, to break the bonds by any simple, low-energy physical methods. (UV irradiation will do, but that is high-energy.)
The other interactions, London dispersion forces, hydrogen bonds, etc. are interactions between molecules. You already have two species that by themselves are in a rather stable, i.e. low energetic, state and you bring these two together. The energy that can still be gained is very minor compared to that obtained by bonding. This is also why this type of interaction is often called secondary interaction.
A second reason is the distance. As you note, most of these interactions can be explained electromagnetically. However, the distances between molecules are typically significantly larger than the distances between atoms of a molecule. Since electromagnetical interactions decline exponentially with rising distance, these forces are a lot weaker at higher distances.
Because the later interactions are just invented to provide a correction to the deficiencies in the description of the complete picture, which is obtained when an approximated treatment of the total interactions is used. That is, you get most of the description from the former (in an approximate way), and to correct deficiencies you add some corrections. These minor corrections are the London, Debye etc.. interactions.