A good non caustic de-greaser will help to lift the oils off the surface with a moderate pressure. You have to be careful with cleaners though as they will breakdown the oils that are in the asphalt as well. Most of the time it will darken and discolor the area you are working in but it will...
If the soot is blocking the air flow of the burner your best solution is to pull the coil and wash it then re-insulate and reinstall it. This will help with the airflow but may not be the cause of the problem. Make sure your fuel filter is clean and you are operating at the correct fuel pressure...
I had some diesel units in the past and they always started slow like that when they were cold.
For the nozzle issue is it completely stopping or just low pressure? If it is just low pressure the opening you made is too large. Otherwise perhaps there is some debris in the line that is...