Bandwidth is Limited:
If a being can be said to be supernatural, they have aspects that go beyond the known scientific observations humans have ever made, or are even able to make. They transcend the known "laws" of nature. Because of that transcendence, maybe in your story the gods' form of communication don't work with our limited brains.
Compared to a computer, the human brain's input/output speed may be relatively slow:
<PERSON> uses his method to determine how much information the brain can process during lexical decision tasks. The answer? No more than about 60 bits per second. Of course, this is not the information-processing capacity of the entire brain but one measure of the input/output capacity during a specific task.
Source: https://www.technologyreview.com/2009/08/25/210267/new-measure-of-human-brain-processing-speed/
So, there's a potential for neural overload when a potentially infinite being makes contact. They must decelerate their own (potentially infinite) thinking speed and communication speed to match the system they're connecting with.
Depending on the nature of the gods in your story, they may not wish to be encumbered by such inconvenience, leading to another possible way to communicate:
Gods are Multidimensional:
To be able to qualify as "supernatural" it is possible the gods occupy or exist within different dimensions than what humans exist within. A four dimensional being could enter and exit a locked room with you inside it, and do so from more than one direction at once. They could warp space and time with ease. They could remove you from a locked room just as easily as they could remove the locked room from you.
Take this possible scene from Flatland, which <PERSON> paraphrases in his book Cosmos:
Let us imagine that, into Flatland, hovering above it, comes a strange three-dimensional creature which, oddly enough, looks like an apple. 209
And the three-dimensional creature sees an attractive, congenial-looking square, watches it enter its house, and decides in a gesture of inter-dimensional amity to say hello. “Hello,” says the three-dimensional creature. “How are you? I am a visitor from the third dimension.” Well, the poor square looks around his closed house, sees no one there and, what’s more, has witnessed a greeting coming from his insides: a voice from within. He surely is getting a little worried about his sanity.
Source: https://www.organism.earth/library/document/cosmos-10
In your story, if gods exist in higher dimensions (or planes) than humans, they can do other creepy things like see all of the insides of your body at the same time as seeing the outside. They can experience your own thoughts at the same time you do, and they can also move themselves back and forth in time, just as easily as you could roll over in bed.
The gods' potential ability to do this (while also watching all of the cosmos from every angle all at the same time) is bound to produce imagery that makes no sense to a finite human brain. Even a tiny shred of that imagery shared in a brief moment of transparency would be more than a lifetime of memory. Plus...
Gods Know Everything:
Yeah, that's right everything. They know what you ate last summer, on July 13th, and who you were with when you ate it.
To be omniscient is to know all things about all things: all people, every subject, and every thought, as well as knowing literally everything that goes on everywhere, and why it's happening the way it is. This is a corollary to being multidimensional--if a god has infinite mobility throughout all space and all time, they could physically position themselves at a vantage point in every millimeter of the universe, all at once, viewing from every angle.
That means they could replay your highest ideals, your most repugnant thoughts, your greatest achievements, your most horrible failures; anything and everything in between, and you'd have no way to avoid their knowledge of the topic.
If, in your world, the gods decide to use shock value to get your attention, I'm sure that revealing that they know your deepest, darkest secret could instill a genuine fear.
What Do They Look Like:
What does any multidimensional omniscient being look like? One description of the Abrahamic God, YHWH, was of "A smoking firepot with a blazing torch:"
When the sun had set and darkness had fallen, a smoking firepot with a blazing torch appeared and passed between the pieces. 209