What is the role of these beings in the wider context of the universe? Are they somehow Earth-bound or do they reign over all the universe? Obviously they are not infinite beings but I guess you don't have to be infinite to have universal significance or power.
This is only my opinion as a polytheist working in a Buddhist framework. The gods do not in my view, reign over the universe exactly. That isn't exactly the way to say it.
As to their natures- Buddhists have historically tended to see them as inclined to benevolence, though there are exceptions and malevolent deities. Note: gods being inclined to benevolence doesn't mean they're perfect at it, or always good. Like people they can mess up with the best of intentions, or being stubborn and thinking they know best in an enterprise.
The high gods in Buddhism appear in traditional sources to be the deities of Mount Meru, which is the Vedic equivalent of Mount Olympus. In Buddhist cosmology, these gods of the heavenly mountain serve a very similar role to what they do in Greek mythology.
They maintain and uphold the world and it's order. The chief of them is Indra- Greek equivalent: Zeus.
They are mostly protective in the Buddhist context- invoked for protection of the community and the teaching, but it is remembered in several traditional sources that they uphold the present order of the world.
As stated, this is almost identical to their Greek equivalents. In Greek mythology, you may have heard that the Olympians inherited the rule from the Titans, and changed the order in several ways to suit themselves. They then made it their job to maintain that order.
I would say in the wider context of the universe, I don't attribute most of the workings there to the deities of Mount Meru, but to older ones like Brahma. I think a polytheistic creation makes more sense because we observe in nature contradictory elements trying to annihilate one another. These could not have been placed there by a monotheistic deity of one purpose and mind.
A polytheistic framework explains it infinitely better. That multiple beings brought about multiple elements of the Cosmos. I think all the gods of all the world's mythologies likely exist. As a Buddhist, I honor them out of recognition that they are a form of life, and caring for that life. Obviously I don't worship all these deities- it's a distant acknowledgement they are there for many of them.
If I am asked to participate in a ritual for any culture's gods- I will do it as an act of goodwill and kindness for the deity, unless the ritual violates my non-violence ethics.
Not all Buddhists venerate the traditionally held gods in any way, but the texts that talk about them show Indra and Brahma as the two most important- if any could be said to be.
This is said to be because Indra protected the Buddha through his life and took refuge in the Triple Gem due to Shakyamuni's teaching. Lord Brahma also protected the Buddha, and knew him from the moment of his birth- because it is said Brahma took refuge in one of the Buddhas before Gautama.
A final note about polytheistic creation: as a Buddhist I don't believe any of the gods created the universe itself, but things about it and in it. That's highly likely.
