Can the Oregon Construction Contractors Board start an investigation on a company without any written notice?

I do not know of authority for a board like this to begin an investigation sua sponte. If they received notice form an inspecting authority that the work was substandard, that might be grounds for beginning such an investigation. But even in that instance, under a "right to face your accuser" theory, the contractor should be advised what is going on. Boards tend to shelter themselves from this "face your accuser" notion with the excuse that anonymity allows people to come forward without fear of retribution. It appears the statements the board members are making to the current clients are libelous and would be "libel per se" in Georgia, not requiring any proof of damages. It sounds like there is some underlying motivation here like a board member's brother-in-law's being a contractor who needs work. I would suggest a thorough investigation into what is really going on.

I'm pretty sure the CCB can investigate anyone in their jurisdiction without any formal notice to you that an investigation is taking place or on-going, although notice is required before you are penalized or disciplined in any way. The real question here is whether they can be passing these comments onto customers or potential customers without a substantial basis for the comments. If you've been orally notified that an investigation is on-going, than certainly it can be on-going without a formal written notice. However, if a lot of time has passed and you haven't heard anything, and you're worried about the investigation - or, if you're just being investigated at all - you may want to consider the benefits of hiring counsel experienced with contractor licensing.