The phrase in Greek is “βρέχει καρεκλοπόδαρα” or “ρίχνει καρεκλοπόδαρα”.
“Καρεκλοπόδαρα” is a compound word (καρέκλα + πόδι = chair + leg) and it means “chair legs”. This word is not commonly used. The phrase is an idiom, just like “it is raining stair rods”.
The second idiom you heard is spelled “βρέχει παπάδες”. “Παπάς” is a more informal word for “ιερέας”.
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Vasiliki Baskou, Instructor/Director, https://learn-greek-online.com.