Some colleges and universities start admitting students from the waitlist as early as a week or so after the initial decisions go out. But the biggest burst of waitlist activity is usually during the first week to ten days of May, once the May 1 Candidates' Reply Date has passed and admission officials know how many of their admitted freshmen plan to enroll. Most waitlist acceptances happen before the end of May although some are later.
Usually by the end of June, colleges “close out" their waitlists. This means that they notify those who are still waiting that they should not expect to matriculate. However, colleges may also allow a small number of waitlisted students to keep waiting throughout the summer, just in case the “summer melt" is heavier than expected. (“Summer melt" is a term that admission folks use to describe committed applicants who change their minds and withdraw in July or August.)
Highly selective colleges, such as those you've named, commonly keep 1,000 students or more on the waitlist and may admit only a handful of them or … in some years … none at all. A college that admits 90 waitlisted students one year may take 6 the next. It's impossible to predict, but the odds are rarely good.
If you have a child who is interested in remaining on a waitlist, read this information from a previous “Ask the Dean" column so you'll know what the next steps should be: http://www.collegeconfidential.com/dean/tips-for-getting-off-the-yale-waitlist
As you'll observe when you read it, students admitted from the waitlist are often selected to fill some deficiency in the enrolling class. Such deficiencies might include (but aren't limited to): gender, racial/ethic background, geography, choice of major, special talents.
From seeing your email address, I'm guessing that your child is Asian. While many “elite" colleges are flooded with talented Asian applicants, some are not. Of the four universities you named, one (Vanderbilt) actually has a much lower Asian population than most of its peer institutions. (Vanderbilt is about 7% Asian; Rice is 20%; Northwestern 18%; WUSTL 15%.)
So if your child puts a “full-court press" on Vanderbilt, it's possible that s/he might be admitted to bolster the campus Asian population if too many admitted Asian applicants go elsewhere.
This may just be a shot in the dark. If your child is accepted off of any waitlists, it could be for reasons totally unrelated to ethnicity (or I may be wrong about your Asian background to begin with). But “The Dean" is a big believer in playing the odds, so if you are indeed Asian, you might want to put Vandy at the top of the list when you launch your war on the waitlist.