I conjured the Four about twenty years ago as part of a planned preliminary track towards getting exposure to the various levels of the hierarchies. As these tend to interpenetrate across presented systems, Yazata is right in that these names correlate to other powers over the same sphere. For example, Djinas corresponds to the Vedic Agni, but also to Crowley's Ohooohaatan, and so forth. As to identity and appearances, focus on the specific names and their impact on one's auric sphere is more important in the immediate sense.
developped in Renaissance magick.
My belief is that these names originate in post-Paracelsian circles, probably in relation to the Olympic Spirits. I am still looking for evidence, now and then, as to their origins, but they could be coded.
What can those spirits do, what they cannot do?
Broadly, whatever involves the Aristotelian elements and their interactions. This could extend to the Zodiacal sphere, but I there are intermediate forces "above" to which they "answer" or rather, transmit certain phenomenon, internal and external. Familiarity with elemental exercises, such as Bardon's, or maybe Kraig's simplified versions, might give a sense of the psychological elements. But if one wishes to produce phenomenon externally, such wind or hail storms, tsunamis, forest fires or just get rich, one would have to experiment with each one carefully.
My experience is that they can be rather forceful of expression given their sublunar proximity.
In calling them, I used Levi's orations from his Dogma and Ritual (Waite's TM back then). In each separate case I used objects such as an open flame, a bowl of water, incense and a rock as bases for the conjurations, plus pentagrams, divine names, etc. From thence proceeded visions and conversations which enlightened me as to the nature of these spirits but also formed a bond.
In one case, I was directed to make a talisman specific to the spirit - something I still have not done aside from a sketch. Not so long ago, however, in a presaging dream of a couple of Goetia spirit, the King made himself known, gently reminding me of what needed to be done. I'm still getting to it, but I have further questions and little time. I'll consider this thread a further prompt.
Another King (or Queen, as it manifested), gifted me an elemental under the direction of its presiding Archangel. This elemental is still with me to this day, and it is just the
cutest thing. It's "growth" was quite remarkable, it even having its own language... and it has a sister. In fact, in a reverie I saw an entire army of them lurking in a habitat, waiting for me to open some headspace for them. They seem to be patient.