A person can always contact the police and file a police report. However, given that "There have been no threats", the police may not be aggressively investigating your situation as the police likely have more severe crimes that need attention. On another hand, there are many reported cases of prosecutors winning cases against cyberstalkers.
Have you tried searching the phone number at the more popular search engines? Sometimes, pranksters are not careful and call from a number that is in a phone directory or is used in an advertisement. The popular search engines often have much information associated with a phone number. The search engines (such as google and yahoo) are free.
There are companies that collect data associated with a phone number. A private investigator likely can find information associated with the phone number you have.
Phone companies have programs that trace where a call originated. When a customer presses a certain key sequence, the program does the trace and information is, eventually, forwarded to local law enforcement. There likely is a cost to the customer to use this feature. You can look over the information provided by your phone company to see what options are available to you.
Some phone companies have features that allow you to block calls from certain numbers from reaching your phone. The phone companies likely charge money for this service.
Some cell phones have features that allow you to block calls from certain numbers. This feature should be free to use if it is available with your phone.Ask a similar question
File a report with the police over the harassment. Even if they do nothing, you at least have a report on file. Contact your phone provider about blocking the messages. Use Google or reverse 411 to trace the number.Ask a similar question