This pattern strings together two or more possibilities, each marked with のやら, and ends with another のやら or just やら. It is used when the speaker genuinely does not know which is the case, often implying a sense of confusion or exasperation. You will almost always hear it with a final verb like 分からない or 知らない, but the pattern itself implies that uncertainty, so it can stand alone in rhetorical questions.

It is a written and formal pattern, typical of novels, essays, and speeches. In conversation, you would be more likely to say 〜のか〜のか or simply use か. If you use it in casual chat, you will sound like you are quoting a book. Note that with two or more items, the last のやら is often followed by と or nothing, but the structure must be parallel.

Particles like は or が are not inserted after the の. The pattern is set: XのやらYのやら. Do not confuse it with the simpler 〜やら〜やら, which means 'things like A and B' and does not carry the 'I don't know' nuance.