I want to sell 1 of 3 condos I own. The first is paid off. The 2nd and 3rd condo units have mortgages. Each condo has a different property address. Could I take the cash from the sale and start to pay off the 2nd and 3rd condo mortgages? Would this defer the capital gains tax until I sold the 2nd and 3rd unit?

This will not qualify for 1031 exchange treatment.  You are selling real estate and paying off a mortgage, which is not an acquisition/purchase of a real estate interest.  You would have to acquire other like-kind replacement property.