I have a 30-year zero-coupon treasury strip that matured this year. There are no records from the purchase in 1992. How do I determine the cost basis?

If you hold a Strip until it matures, the cost basis and maturity value should be the same.  The formula for calculating cost basis is the amount you paid originally plus the interest on which you paid tax every year.  Adding those together gives you the maturity value the same as your original purchase price.

OID is a form of interest. You generally include OID in your income as it accrues over the term of the debt instrument, whether or not you receive any payments from the issuer.
In the case of a zero, this is called imputed interest.