"Deal with" is neutral or occasionally negative. You can "deal with" a problem by addressing it, which may require some distasteful work on your part or it may not, for example:
- I'm going to deal with the dishes after dinner — neutral. There is an issue (dirty dishes) and you will take care of that issue, but it isn't a big deal.
- Fat Tony is a squealer. Deal with him — negative, the implication is to "solve" the problem by killing Fat Tony.
You can also say to someone "Deal with it" when they complain about a situation, which is telling them to accept the situation and stop whining about it.
"Addressing the unemployment crisis" is essentially synonymous with "Dealing with the unemployment crisis." Both imply actually doing something useful.
"Grapple with," as your definition implies, is generally stronger and implies a struggle of some sort ("grapple" comes from the same root as "grab" and "grasp" and literally means to seize hold of something). It is used for more existential things; you would not say "I'm going to grapple with the dishes" except maybe as a joke. Instead it is used for problems that you have to think about, for example a software bug or a tricky research problem or (in your example) the unemployment crisis.
"Grappling with the unemployment crisis" does not necessarily mean anything useful is being done. It just means people are debating and researching the problem.
"Tackling" is literally closer to "grappling with" (it means to knock someone down or to grab onto someone and pull them down) but metaphorically is more similar to "dealing with" and "addressing." It is a little more forceful, though. It carries the imagery of someone (or some group) rolling in and working on the situation with little to no debate or waffling about.
It is also used when the task is relatively large; if there was only one meal's worth of dishes in the sink you would say "I will deal with the dishes" but if you haven't dealt with them in four days and they've really piled up then you might say "I will tackle the dishes."