Basically, the Organians were corporeal beings. Then with time and according to their desire, they evolved into non-corporeal beings.
In the same way that the Federation does not come into contact with the civilization of a planet if it is not evolved enough, the Organians watch the species evolve without interacting with them even if their lives are in danger.
Before to know their true nature, the Organians were rated Class D-minus on the Richter cultures scale.
They often exhibit a great deal of apathy and feel little concerned about the fate of the rest of the living in the galaxy. They often have to be jostled in order to be involved in an interstellar conflict to finally end it.
Organians can show geolocalized omniscience at times when their world is hit by an event.
They can awaken the dead by resurrecting them. They can take control of the bodies of other living beings. Alter the memory of living beings. They can appear at several places at a time, at light years away.
Their life expectancy is unknown, but they may be immortal. They can live at least several thousand years.
It is impossible to know what they looks like in reality. They have no body envelope for millions of years. The intermediate state before turning into humanoid is an intense light energy ball.