Yes, if you're an "at will" employee. Your employer doesn't need a reason to fire you, or give you any notice, and they can change your job duties or reduce your hours or demote you, all without notice without reason (and you can quit on the same basis).
If you have a written employment agreement that limits the employer's right to fire you, or you belong to a labor union that protects you, then you're not "at will," and the employer may not be able to do these things.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
If I understand your question correctly, you are saying that your employer simply changed your rate of pay and your position without notifying you in advance. While it is true that, in California, unless you have a contract or are protected by a union, you are considered to be an at will employee, that does not permit your employer to promise you one rate of pay and then pay you another after you have already performed the work. The employer is permitted to tell you that for work performed from that point forward your rate of pay will change, but the employer has to pay you for work already performed at the rate you agreed to accept. Your choice then is to either accept the pay change or find another job.
As to the position change, if you are an at will employee, then the answer is “yes,” your employer is permitted to do that without having you sign paperwork.
Disclaimer: The response given here is not intended to create, nor does it create an attorney-client relationship. Nor is this response intended to be anything other than the educated opinion of the author. This response is based on the limited facts presented, and should not be relied upon as legal advice. To the extent additional or different facts apply, the response might change. This response does not create an ongoing duty to respond to questions.