Can there be a displacement currents in the air and if yes, can they transfer any significant energy on a relatively long distances? Something like 50-100 meters? What could be an efficient way to create a displacement currents in the air? Perhaps use the resonant frequency of the air molecules? What about the soil?
For the sake of getting an answer out, I'm going to assume that the "displacement currents" you refer to are in fact the displacement currents that are discussed in connection with capacitors and Maxwell's equations.
With regard to the first part of your question: "Can there be displacement currents in the air" then the answer is technically yes. Displacement currents do not have any limitations as to where they can exist.
Now on to the other part of your question: ". . .can they transfer any significant energy on a relatively long distances". The answer to this, as far as I can imagine, is no, not really.
Displacement currents are not an ordinary part of power transmission in the basic or practical sense. They come up in physics as a starting point for a number of highly theoretical arguments about what technically can and cannot happen in the universe.
To put it in perspective, I have never once seen an ammeter whose purpose was to measure "displacement current" nor can I think of any device that uses them off hand. To make a very rough analogy, they are a bit like that proverbial tree that falls in that proverbial forest with no one around. They get discussed because they are a mathematical possibility, not because they have any practical significance in power transmission or device construction.
If I have overlooked something, somebody please feel free to weigh in.