I'm guessing the build up of oil is from the lack of spark.
Have you checked to make sure the flywheel is seated properly and not loose? A loose flywheel will cause all kinds of issues.
Once you've determined that the flywheel is not the culprit, then I would move on to the electrical.
Have you checked the tabs that hold the coil on? they should be bare metal to help with grounding.
Generally the coil is either good or bad, I've never seen an in between.
The CDI can however produce intermittent spark.