〜やら〜やら
what with … and …; all sorts of
Noun / Plain form + やら + Noun / Plain form + やら
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やら〜やら lists examples from a chaotic or overwhelming situation: 引っ越しやら仕事やらで、忙しい, "what with the move and work, I'm really busy".
It's like とか〜とか, but with a sense of things piling up and being hard to cope with. It's often followed by で to give a reason, or by a word like 大変 or 大騒ぎ.
It can mix conflicting feelings: うれしいやら恥ずかしいやら, "happy and embarrassed at the same time".
On its own, 何やら means "something or other", a vague "something": 何やら変な音がする, "there's some strange noise".
Examples
引っ越しやら仕事やらで、忙しい。
What with the move and work, I'm really busy.
うれしいやら恥ずかしいやらで、顔が赤くなった。
I was so happy and embarrassed that I went red.
泣くやら叫ぶやら、大騒ぎだった。
What with the crying and shouting, it was a real commotion.
何やら変な音がする。
There's some strange noise or other.
宿題やらレポートやらで、寝る時間もない。
What with homework and reports, I don't even have time to sleep.