EM waves are created by accelerating electric charges, as happens when current suddenly flows between oppositely charged objects and those charges redistribute themselves. So whenever a spark "jumps" between the globes of a van de Graff generator, an electromagnetic wave train is produced, containing a broad spectrum of random frequency components. If you produce such a spark near an AM radio receiver it will produce a sudden burst of "static" (a sharp, brief crackling noise) from the radio speaker.
Lightning bolts will have the same effect on an AM radio; in this case the radiated electromagnetic waves are so strong that a radio can pick up these static bursts from a distance of many miles. Special radio receivers and antennas can be installed in aircraft to allow the pilot to identify the direction to the lightning source, and steer the plane to avoid the lightning.
Electromagnetic pulses of enormous power are also produced by the detonation of nuclear weapons. In these cases, the burst is so strong it will actually destroy radios and other electronic devices many miles away from the explosion.
If you model a segment of a spark channel in air as a piece of wire, it will radiate EM waves just like a wire antenna would. But since a long spark channel is bent and twisted in all directions, the radiation it emits will be radiated in all directions too.