Early Thirsty: Suggestions for Plagiarism-Checking?

This thirsty is prompted by the post from the LA Times article about essay mills and cheating. In the fall, I'm the grading assistant for a prof who has a reputation for not giving a flying f*ck about plagiarism. He assigns the same essay topics year after year, and it's rumored that students simply pay students who've taken the class previously for essays that passed. He has a different grading assistant every year, so this stuff is hard to catch. I'm sure the students plagiarize from other sources as well.

As the grader, I plan to be tough on plagiarism because A) I think the students should actually try to learn something by writing their own essays, dammit and B) it annoys me that this particular prof is giving our department and our discipline a reputation for being "easy" with his super-lax, anything-goes reputation.

Unfortunately, our university has an "honor code," and therefore officially believes that students will never cheat. Hence, there is no institutional funding for a subscription to Turnitin.com or similar plagiarism-catching websites.(Apparently nobody's heard of "Trust, but Verify" around here.)

So, the thirsty:

Q: How do you vet students' essays for plagiarism? What are the "clues" that I should be looking for? Are there websites where I can do plagiarism checks for free?