Disable the EHA and drive it temporarily to see if the problem goes away. That way you will know if it is mechanical or electrical. If after disabling the EHA you still have the problem then obviously it has nothing to do with the EHA.

You can disable the system by simply disconnecting the O2 sensor. You will get a check engine light, but it will go away when you reconnect it. Be careful with any connector that you remove because the car is 15 years old or so and they can be brittle.

Your oil pressure worries me. Has this engine had frequent oil changes, how many miles, how has it been driven?

Good luck,