IMHO:An activity involves is a wider term and it may or may not involve exercises, it �s what ss do (speaking activity, writing activity, group activity)
Task is usually stated instructions at the beginning of an activity/excercise, e.g. "Listen to the dialogue and fill in the missing information"
An exersice is a set of questions/sentences that test your knowledge/provide practice.
Here �s what the dictionary offers:
task- an activity which is designed to help achieve a particular learning goal, especially in language teaching
actity- a thing that you do in order to achieve a particular aim
exercise-1)an activity that is designed to achieve a particular result
2)a set of questions in a book that tests your knowledge or practises a skill
All of which sounds pretty confusing I guess:)
Maybe someone has a betterexplanation.
Sophia