The term is drum trap and yes if your gouse is that old you probably have one. They were before the Ptrap and unfortunately for you are difficult if not impossible to clear a clog with a cable.
I suggest to cut it out and replace it. If you are not a handy type of person, its best done by a plumber. In the KC area the going rate would be about $300-500 depending on access to the rapair and company used.
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