How can I find a website that will discover plagiarism from specific
phrases in student papers which students have bought from sites that
sell term papers of other students?

Hello.

Plagiarism.org is a leader in this field.
http://www.plagiarism.org

A related site, Turnitin.com actually provides the technology that
will discover plagiarism from phrases from papers students have bought
online. For more information, visit:
http://www.turnitin.com/

Another service is called PlagiServe:
 http://www.plagiserve.com/

Edutie offers similar services:
http://www.edutie.com/

You might also want to take a look at WCopyfind, which provides
software to detect plagiarism. For more information visit a web page
at the University of Virginia:
http://plagiarism.phys.virginia.edu/Wsoftware.html

A similar software package is called CopyCatch:
http://www.copycatch.freeserve.co.uk/
Glatt Plagiarism Services also offers some software packages:
http://www.plagiarism.com/

Another software package is the Essay Verification Engine (EVE):
http://www.canexus.com/eve/index.shtml

An Oxford web page has a comparison of some of the more popular
services:
http://www.oucs.ox.ac.uk/ltg/reports/pappendix1.html

For general information on the subject of plagiarism, visit The Center
for Academic Integrity:
http://www.academicintegrity.org/

Also see the web page Combating Cybercheating:
http://www.epcc.edu/vvlib/cheat.htm

search strategy: plagiarism.org, turnitin, cybercheating

I hope this helps. Good luck.

You might consider asking authors to turn in their notes and outlines
in addition to their finished manuscripts.  I suppose I am trying to
answer the "what happens next" question, in the event that a piece of
software says plagiarism has occured.  Certainly, one would expect
that the author should be able to appeal the ruling of a piece of
software which might be in error.

If authors are told in advance that they should either turn in or save
their notes to support their claim of original authorship in the event
that plagiarism is suspected, you will have communicated that it is a
serious matter that your are vigilant about.

One of the problems with programs which track "word order" as a method
of detecting plagiarism is that there are many ideas with only a
limited vocabulary pertaining to them.  If you ask a thousand people
to create a verbal image of a sunset, you can bet more than one of
them will say "The sky turned a blazing gold."  Even if the phrase is
used by only one out of a hundred, that will still be "ten plagairized
hits" from some software.

In some fields, such as history, a system like that would be a
nightmare.  The Battle of Hastings has two points of view, one from
the winner and another from the loser.  Any other description of the
battle scene is limited by geographic and historic constraints. 
Between these two points of view and the restraints of history and
geography, the subject has been written about thousands of times. 
Because of the limitations, it is not only possible, but probable that
the exact phrasing for a sentence or even for a whole paragraph has
been used more than once.  There are only so many things to be said
about a limited knowledge subject, and when thousands are saying it,
repetition becomes almost as common from original research as it does
from plagiarism.

A little care needs to be taken with these programs and allowances
made for the subject matter involved.