TOEFL does not boost application. It is a pass/fail kind of thing. As long as you can prove that your English is in working order - you're good. TOEFL WILL NOT be chosen over GRE in any way and will not compensate any deficiencies of the GRE score. If you can waive the requirement - just waive it. Sending the TOEFL score will only cost you money.
I think you could also just provide them with the unofficial copy or screenshot of your scores and indicate that if they want the original results you can send them. I didn't have to take it so I'm not completely familiar with how it works.
Would you be interested in obtaining a PhD in something other than sociology? If so, then I don't see the harm. If you have absolutely no desire to accept a position in any other department, then no. Adcomms usually don't have trick questions in their applications.
I'm not at all familiar with Sociology, but in many Biology departments they will do this because 1) the programs are typically very interdisciplinary and 2) people often might "fit" better in a different department. As a personal example - I applied and got into a Human Genetics program, but switched to a broader Genetics and Genomics program halfway through my first year since it was a better fit for my research interests. The programs themselves (in my experience) are often so similar that applicants may not realize a different program is a better fit for them.
I'd say it definitely couldn't hurt to have your application shared with other programs - even if you'd prefer to get a degree in Sociology. Having more faculty look at your app is never a bad thing!
I just had a professor who sits on admissions committees look over my SOP.
My introduction was talking about how I liked to go to museums as a child and was fascinated by the ancient world. He said that starting out like this is a huge mistake. Obviously if you are applying to study archaeology at the graduate level, it's pretty much assumed that you're fascinated by the ancient world and probably enjoy museums. But so do lots of people. What makes you unique. Attempt to illustrate your passion for the field without really telling some kind of silly story about your childhood. This is also an approach that many people take, and if you really want a strong SOP you'll find a better, more mature, and more creative way to say it.
The next point is, whether or not to talk about the negatives on your application. I wrote mine this year mentioning them extremely briefly and moving on. My thought behind this was to simply focus heavily on all the points that make me a competitive applicant. However, some graduate programs explicitly say that your SOP is the place on your application to mention your negatives and why the committee should overlook them. Obviously, this should not be the focus of your SOP. What the committees are looking for here is growth and improvement above all. Do not make excuses for poor grades, weak GRE scores, or a spotty work record. Do, however, point out how you have grown, how the committee can see improvement, and then highlight the things that make you a fabulous candidate.
The last thing I will mention is also very important, particularly for PhDs. Make sure that you know who you are applying to study under, and what your project is. Demonstrate that you would fit into the department like a glove and that you read Dr. Octopus' latest article on the newest theory, etc. etc. etc. Also, have a concise project in mind. Remember, you're not married to this idea, but you need to show the committee that you can ask the right kind of questions concerning your proposed research and that the project is something that the faculty could help you on based off of their interests and previous work. Do not make this project a carbon-copy of something they have previously accomplished, but a project that complements the research they have already performed. It is also highly advisable, since your job as a PhD student is essentially to perform lots of independent research, to demonstrate that you are capable of performing independent research. Although you want to show that you are a good fit for the program, you do not want to appear as though your adviser will have to hold your hand for the next five years.
Hope that helps! I'm no expert, but these are simply my thoughts on the process.
