What is the usage of orbitals more complex than f orbitals?
Surprisingly, I learned that there are also usages for orbitals g,h,i
  and even j.


Actually, the letter "j" is not used, so it is s, p, d, f, g, h, i, k, l, etc.

The higher angular momentum orbitals do enter the domain of science, due to excited states of atoms. Transitions to and from excited states are observable through atomic spectroscopy.

For example there is the article Microwave spectroscopy of Al I atoms in Rydberg states: D and G terms