Since I loaded Office 2015, nearly every file I open from an outside source (e-mail) opens 'read only'. I have tried to find a setting in Preferences without any success. It happens in Word, Excel and Powerpoint. Any ideas?
Since there is no "Office 2015", I assume you're referring to Office 2016? If you're receiving Office files via email and they're read only, perhaps the sender has sent them as read only. There are times when files sent from a Windows machine to a Mac might have an ownership tag on them. That can occur when transferring files from NTFS to HFS+.
What version did you purchase? Office 2016 on a Mac is only available as part of a 365 subscription or as Office Home & Student. The home and student is a one time payment for use on 1 mac only. Office 365 is either a monthly fee or a yearly fee.
From your description, my first impression was that you have not licensed your copy. However if that is true you shouldn't be able to edit any documents, not just ones you have received. That is still my guess as I can't think of another situation other than what chscag said.
Edit: Maybe Brian is onto something. He posted while I was typing.