Hi Monica, these words are almost interchangeable, but not quite. They all mean approximately the same thing, but 'cope with' and 'deal with' usually imply some degree of difficulty that is being overcome, more so using 'cope with' than 'deal with'.
E.g. She found it hard to cope with a full time job and looking after her children.
It's difficult to deal with people who are very drunk. / The police have to deal with many different problems every day.
'Manage' and 'handle' don't necessarily imply difficulty, but may do so.
E.g. He manages the team very well. (Basically, he's the manager - normal verb usage.)
She managed to get home just in time for the children.
He didn't manage to do the housework very well.
He handled the situation very well.
Hope this helps!