Can my employer make me sign an agreement not to sue it in exchange for a severance package?

Yes.  Although it is possible that the law is different in Oregon, in the jurisdictions in which I practice your employer has no obligation to provide you with a severance package unless you have a contract which says otherwise.  Thus it is within its rights to demand something in exchange for severance compensation, including a release of any claims.  Such a release would be enforceable with regard to most claims unless you can show some reason why it is invalid - that it was procured by fraud, through duress, etc.  There may be some claims, for example age discrimination claims, for which the release can be revoked within a certain period of time.  Of course, if you revoke the release or it is found to be unenforceable, you have to return the severance pay.