Common OBDII codes after swap

not if you have the pcm correctly flashed to turn off extra O2 sensors, emissions and leak detection pump.

You are now running in "limp home" mode, which causes the pcm to stay in open loop ie no O2 control, so you will get lower HP, MPG and a host of other issues. You will need a speed sensor and flash to remove O2 heater relay codes.

Doubt if O2 codes are from oil leak, that would give you a code of O2 volts low, not high. Your pcm must be a CA spec rather than Fed spec. Really surprised you dont have LDP code, Evap leak code and batt temp code...possibly not setting them due to O2 codes keeping it from closed loop. It might not set emissions codes until it coes into closed loop, depending on what year pcm is.