Hi, Welcome to Just Answer!
Oil smoke (blue) or coolant smoke (white) will not cause your vehicle to fail emissions test. If you have Fuel Smoke (Black) this will fail you. This is caused by a rich running condition.
First place to start would be a complete tune up and if there is a check engine light on, have necessary repairs made to turn light off.
If this is a carburetor engine, you may also need to have the carburetor tuned and the ignition timing set.
Witht he O2 Sensor disconnected the engine will smoke. Replace it. Also, you may need to change the oil as the extra fuel that is being forced into the engine because the O2 Sensor is missing may cause it to become contaminated and add to the smoking. The is no temporary fix for a smoking engine.. No need to worry about the smoke if it isn't black. But the missing O2 Sensor needs to be there!
If it has any codes Autozone will check them for FREE!