The leaving it outdoors idea is good. Obviously not in direct sunlight or any extreme conditions.
I suggest cleaning it carefully too.
I had this problem with an old (electric) guitar I bought on ebay. It reeked. I disassembled it, scrubbed it, scoured it. I used soap, all sorts of commercial cleansers and also vinegar. I did all this for an entire year. Finally, leaving it out in the garden for a few hours a day did the trick.