No, the options don't trade on the NASDAQ and most certainly not on the OTC. They are issued by the Options Clearing Corp. and trade on these exchanges:
American Stock Exchange (AMEX) Boston Options Exchange (BOX) Chicago Board Options Exchange (CBOE) International Stock Exchange (ISE) New York Stock Exchange (NYSE/ARCA) Philadelphia Stock Exchange (PHLX)
One of the requirements to be "optionable" is that the underlying stock be listed on a major exchange. Once a stock is delisted it no longer meets that requirement and OCC will not issue any new series. But the series already out there will continue to trade until the original expiration, as long as the underlying shares themselves remain tradeable.
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