Yes I think I understand your "oscillations"

What you are most probably referring to is chattering.

This can be caused by a poor regulation of the power supply.

What happens is this :

(I assume that the solenoid power is drawn from the unregulated side of the MCU power supply )

1. MCU powered up. Things are fine.

2. You give a command to energize solenoid.

3. solenoid activates and pulls the MCU power supply down or its own supply.

4. MCU resets and or solenoid drops out due to low voltage .

5. Once the solenoid drops out, voltage picks up again and you start all over from step 3.

Would the above be possible ? If you access to an oscilloscope you can "see" the chattering glitches.

Raghu