To answer your question: it sounds like you have a very good case if you can show that your competitor is the one who engaged in this conduct. Usually this type of attack is done anonymously or through others.
But if you do have proof that he is behind these efforts, then you have a very good case of trade libel, not to mention what is called libel per se against you. This is because he has accused you of committing a sex offense. That means that you do not have to show "special damages" which would be, for example, lost business, though it appears you have that as well. You could probably also obtain an injunction under the Illinois Deceptive Trade Practices Act which provides "A person engages in a deceptive trade practice when, in the course of his or her business, vocation, or occupation, the person... disparages the goods, services, or business of another by false or misleading representation of fact." Given the clearly intentional and malicious nature of these attacks, I also suspect that a court would award you attorneys fees, which are allowed under the Act in the discretion of the court. This would also be a violation of the Illinois Consumer Fraud and Deceptive Business Practices Act which allows you actual damages, punitive damages, injunctive relief and attorneys fees.
Things to do:
First, you can contact the Illinois Attorney General's office The website is http://www.illinoisattorneygeneral.gov/consumers/. They investigate violations of the Illinois Consumer Fraud and Deceptive Business Practices Act, though they are more focused on consumers than businesses. Since there are others that are being victimized by this guy, you should get together and all complain about him.
Second, you can sue this guy whether or not the Attorney General's office decides to do anything. (Don't blame them if they don't. They work very hard and need to prioritize the cases they pursue.) But then the practical issue that you will be faced with is whether this guy has any means of paying a judgment--whether it is for damages to your business and reputation, or for the attorney fees you will incur in suing him. Also, in my experience, people as unscrupulous as this fellow appears to be, will have no problem lying to the court, and, if he loses, hiding his money and assets from attempts to collect.
But again, given that you say he has done this to other persons and businesses as well, it may be a good idea to contact his other victims band together and hire an attorney to represent all of you, so that you can share the cost of a lawsuit necessary to stop this outrageous conduct, and, hopefully, recover the damages he has has caused you.
Go to a business attorney. Bring an action for an injunction to require that this company cease and desist. It would be hoped that a 30 day letter demanding that the conduct stop would be respected. However, based on what you are saying this may well not be the end of the conduct. You should seek not on only an injuction but also damages for intentional interference with your business.
This answer is provided for informational purposes only. Actual legal advice can only be provided in an office consultation by an attorney licensed in your jurisdiction, with experience in the area of law in which your concern lies.
Agreed - a commercial litigation attorney may be the way to go to press the issues of libel, tortious interference with a contract, and any other applicable causes of action under your state's laws.
A roundup of the best tips and legal advice.