I do practice in your state. A landlord is required to give 30 days notice to cancel a month-to-month lease. I believe the same requirement is place on the tenant, although I would have to read that specific law to be sure. Keep in mind that a 30 day notice is often more than 30 days. The notice required is essentially on monthly rental period. So, if you pay rent on the first day of April and you give your 30 day notice after the first day of April, you cannot cancel the lease until the expiration of the next full rental month, which would be the end of May. Right now you basically have an implied month-to-month lease since you have been operating that way after the expiration of the previous written lease. The law will imply the same terms as were part of your previous lease, but it is now month-to-month.
A landlord and a tenant can negotiate outside of the general law if they both agree to different terms. Outside of provable discrimination based on race or national origin, I do not believe that just because a landlord gives a break to one tenant, he must give a break to every tenant. Your best bet is to point out that you have been a good tenant and that you need to move sooner than 30 days.
If you do move out without giving proper notice, the landlord would be entitled to the last month's worth of rent that you did not pay. Whether he/she decides it is worth the time to try and collect on it is another question. However, if he/she is holding a deposit, they will likely deduct it from the deposit. Whether the landlord reports this on your credit is entirely up to the landlord. I would only be speculating given that I do not know your landlord. Good luck.
I am not licensed in your state, so I would consult with an local attorney on this matter. However, I am under the impression that Arizona, much like other states, converts the tenancy post lease into a form in which rent is conveyed, which in the vast majority of circumstances is month to month. In a month to month tenancy, a 30 day notice to vacate is required despite the lack of a written lease. Good Luck!
Our out-of-state contributor is correct: when the written lease expired and you stayed, you went automatically into a month-to-month lease with the same terms as the prior written lease. You will have to give the 30-day notice because the written lease probably required it and because the Landlord-Tenant Act requires it whether the prior lease did or not. And remember that that is 30 days from the next rent pay date. To get out by April 30, you have to give written notice by March 31 or earlier.
Can the landlord hurt your credit? Yes. If you leave damage behind, that comes out of your security deposit. If you don't pay for the entire period of the required notice period (e.g., you leave March 31 without prior notice and without paying for April), the landlord can use your security deposit to reimburse himself for unpaid rent. If these amounts exceed your security deposit, the landlord will probably seek the difference. If you don't pay it, he is likely to make a negative credit report.
There is nothing prohibiting a landlord from treating tenants differently in the way you say.
You need to consult with an attorney who is knowledgeable about both landlord-tenant law and consumer protection law.