I don’t think its the most obscure, but a very rare way of communication, which uses technology, is when people are so severy paralysed that they can no longer speak or communicate. In such cases brain-computer interfaces can be used, which work in a similar way to the last demonstration shown in the second Christmas lecture.
Such systems have flashing groups of letters and a computer can tell which letters the person was to select. By selecting letters one at a time, words and sentences can be written and then the computer vocalises what the person wants to say. This technology is only used at the worst cases as it is one of the slowest way to communicate!
So I don’t know about humans, or about animals, but if you want to communicate with a computer there’s a set of languages called ‘esoteric languages’ or esolangs. Some of these are really obscure! For example, there’s one called Whitespace where only spaces, tabs and carriage returns have any meaning. Others, like piet, are based on pictures.
I think there are many ways that animals communicate that we have no idea what it must be like, for example using sonar in bats. For a long time, people just did not think this could be possible, then when it was discovered how it might work it radically changed our view of things. Another weird way of communicating is what results in a thing referred to as swarm intelligence when groups of simple animals act together in a way that would be only possible by a much more complex organism. you see this with insect like termites. individually not very bright but collectively can communicate to really solve very complex problems
Almost by definition perhaps the most obscure methods of communication we probably haven’t discovered yet, because it is so alien to us, we haven’t started to think that animals could communicate this way.