How removing the catalytic converter affect the oxygen sensor?

With any vehicle modern enough to have a catalytic converter and oxygen sensor, removing either or modifying the emissions control system in any way is not advisable. Because the components of the system are so interrelated, chances are very high that you will force the system into "limp home mode" since it is not getting proper information from a sensor. The car will keep running and you may notice no difference in driveability but you will likely experience worse gas mileage and possibly shortened engine life. Keeping it stock is the only smart ( and legal ) thing to do.