You mean here using those verbs in relation to a problem or a matter in particular,because otherwise 'address' and 'handle ' could have other distinct meanings. 'to address' means to deal with a problem or a matter by thinking carefully about it and doing things to improve the situation. 'to handle' involves taking action as well to deal with a situation ,a person or anything that is seemingly difficult 'to deal with' is both handling and addressing a situation . It is thinking about it and then taking the required action . 'to cope with' is almost the same meaning as 'to deal with' and it has to be a difficult situation. As you see they are somehow close in meaning and in many times synonyms and could be used interchangeably.

Address can mean to put a mailing address on something. Address means to find a solution (even if only temporary) to a problem. Cope with means to bear the physical and mental stresses involved. Deal with can also be used to mean that. It can also mean to address. Handle is the same as deal with when talking about a problem. Handle can also mean to operate or control. For instance, you can handle a horse or car.

Address a situation and deal with a situation mean the same, whilst cope with someone/something and handle someone/something mean the same