Letters of interest are used to say that you're interested in a particular program. They're not very useful unless you don't seem to have much of a connection to the school - demonstrating interest by writing, however, may draw enough attention to get you an interview.
Update letters are for notifying the committee of new activities/accomplishments you've made.
In the area letters notify schools you'll be in the area around a certain time, and some people say that doing so may get you preferential consideration for an interview. More than likely that's BS, and it's just a coincidence they got an interview offer after sending a letter in, but the ITA email could speed things up a bit so that you can string a series of interviews together (if you get a bunch of offers).
Letters of intent state that, if a school accepts you, you'll withdraw from everywhere else and go to that school. This is a pretty big deal, and while probably not legally binding should be taken pretty seriously. Usually you send this in if you're waitlisted at your #1 school, and you send it sometime in the new year. For schools this allows them to solidly fill places in their class without having to worry about more turnover. This may be most effective between March and May, when the non-rolling schools announce all their decisions and the scramble for placements begin.
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You can combine letters together (send an update letter + letter of interest + in the area letter, all in one email). You should have a pretty solid update prepared (updating to say you got an A in this class may be irrelevant to the committee, and thus could be annoying) - consider how the school parses updates, and plan accordingly. If there's the amp secondary processing system online, for example, then you can just upload updates without troubling anyone; if you have to email or physically mail the letter in, then make sure it's serious.
With regard to your personal situation, do you have a substantial update? LORs are attached via AMCAS, typically, and so wouldn't really seem to qualify for any of the above categories (as in, writing them a letter saying that you're sending them LORs they've already received from AMCAS may not be very productive).
That being said, your style is up to you. Some on SDN will call schools to ask what their application status is weekly, and some refuse to contact the school ever.
