Consecutive= periods of time (days, years, months) that run together, Example: The Yankees won the World Series in consecutive years more than any other team. December, January, and February are three consecutive months. Best, better, very good are the consecutive grading scale on my brother's website.
Continuous=(more of a scientific word) an adjective describing an action that never ceases. Example: Sharks are said to be in continuous motion, even when they are asleep.
Continual=also an adjective, also can be used as an adverb (continually). Continual describes something that happens over and over again. Example: Do to continual speeding violations, the driver had his license suspended. The continual noise complaints from his downstairs neighbor was the reason he was thrown out of our apartment building.