An anonymous commenter asked how we evaluate faculty applications. While it's a little late, it's a valid question, so here are some high-level thoughts. Here I'm speaking only for myself, of course.
First, I should point out that ideally, we're not reading your application from scratch -- we already know you. We've seen you give a talk we like, or enjoyed one of your papers, or otherwise formed a (positive) impression. The most important things you can do when applying come well before you write up your application. If you're not taking advantage of opportunities to make yourself known in the community as a graduate student, you're not doing your job. [Obviously, we don't only look at applications of people we already know. But that just makes our job harder, and makes it harder for you to get picked out of the crowd.]
After that, it's not exactly rocket science. I'm looking for a strong record, and the first things I'm looking for are good publications and good letters. Applicants on the first pass are usually sorted into 3 basic categories: invite for an interview, decline, or study further. The publications and letters are the best guide for what pile you'll go into.
Once the pack is cut down, more details will come into play. Some of us will probably read your papers to get a better idea your work. Natural more detailed questions come up: How interesting is your work? How well do you fit our department needs? What teaching experience do you have? Is Harvard a place where we think you would be successful? (For example, what other areas of Harvard might serve as possible points of collaboration?)
The interview helps us answer these questions further. At the end of the day, what we're deciding is if we want you as a member of our department. Research quality is a primary issue, and usually the primary issue. But at this point, hopefully all of the people we're looking at have high-quality research records, with results that we collectively find compelling. So the secondary issues I mentioned -- are you a good fit for us, are we a good fit for you? -- do matter.
In the end, I don't think there's too much you can do to "strategize" your application -- because the main issues are to have a good work record, get people who can write you good letters, and be an interesting person who seems like they'd make a good colleague. I expect that's not surprising anyone. Though I'm sure since I wrote this a bit hurriedly, someone will point out where I've not described things suitably carefully or in enough detail.