All of the words refer to taking care of something. They only differ in the situation in which they're used.
When I hear "cope with", I think about someone dealing with something like an illness or a difficult situation. Ex: He's coping with his mother's passing very well.
"Handle" is simply taking care of a situation. Ex: He's handling his new responsibilities at work with ease.
An alternate definition of "handle" can be a grip attached to an object for using or moving the object, such as a door handle. You can also "handle" objects.
"Tackling" a situation implies that you're taking care of the situation with enthusiasm or vigor.
Ex: He tackled the project full-force and had it done by yesterday afternoon.
Using "address" is similar to using "handle" in that you're simply taking care of the situation.
Ex: She addressed the grieving mother with grace.