Why isn't 'ciuchy' correct?
"Ubrania" is a standard word. But you're right "ciuchy" is a quite common colloquial word.
Can't we omit "oni" (they) in the polish sentence?
You can always omit "oni/one" in polish sentence. It is less common than omitting ja/ty/my/wy.
I wrote one instead oni. How was I to know gender?