Can't help but can offer a suggestion.

Do you have call tracking software installed in your phone system? Or at least can you track the SMDR feature of your phone system to see if the calls are actually making into your phone system? Match up the times to SMDR to confirm.

One other thought is that it could be some type of an LD reseller. A company that could provide LD voip services from computers. If someone uses their computer to make calls, (something like Skype) this could be one of the nodes that calls originate from.

Can't figure out the night time calls unless you have voicemail taking messages from the caller.

Tip and ring, the work of the devil!