Thank you for your reply, and I apologize for not getting back to you last night, but I had already logged off for the day by the time you responded. Oregon law on non-solicitation and non-compete agreements, like in most states, is very complex and ultimately only a court can make a determination if a dispute arises involving the signing or enforcement of one after evaluating the language of the agreement, the circumstances of the signing and any issues involving enforcement.
That said, the law is very restrictive in Oregon. There is a non-compete statute that severely restricts when a non-compete agreement can be considered valid. One of the requirements is that in order for a mid-employment non-compete to be enforceable, there must have been "...substantial bona fide advancement of an employee within the company..." at the time the non-compete is signed. A fairly recent case has applied the non-compete statute to non-solicitation agreements that are drafted broadly. I have included two very good discussions of the statute and the non-solicitation application below for your review. There are many more restrictions in the statute as well as to the scope and who can be included in a non-compete, but since they are too numerous (thus the complexity) to list here, I would ask that you read the information at the link to see what they are and I will also include a link to the statute itself.
Assuming then that your situation falls outside the allowable circumstances for a valid non-compete/non-solicitiation, then, although Oregon is an employment "at will" state, it would normally be deemed unlawful to terminate an employee for refusing to sign an unenforceable agreement. That said, they might terminate you and then you would have to sue for wrongful termination, which can be expensive, especially if you are unemployed. One other option is the sign the agreement, remain employed, and then when you are ready to leave, hire an employment law attorney to file a petition to have the non-solicitation agreement declared unenforceable by the court for violation of the statute. That way, you can job search and work without the threat of an injunction and law suit. That though is up to you.
The following are the links I promised. I will be gone for most of the day, but if you have follow up questions after reading the information at the links below, please ask and I will get back to you as soon as possible. If none, then if you could take a moment to leave a positive rating in the box above, I will receive credit for assisting you today. Thank you