If you did not have a written agreement with your landlord, then you would be considered a month to month tenant and your tenancy could be terminated by either party on 30 days notice. So, your landlady can ask you to leave. If you have something in writing, that will determine whether the landlady can terminate the tenancy.
As for the process server, he can use deceptive practices to serve you. It may be a little unseemly, but it is more than likely legal service.
If you are being sued for unlawful detainer, you may want to work something out with the landlady so you don't have an eviction on your record. If not, you may need to hire an attorney.
First, I want to know if you have signed a lease agreement with you landlady, if yes, then that contract should prevail. However, if there was no contract you are considered to be in a month-to-month tenancy. wherein your landlady can cancel your tenancy after giving you a 30-day notice. As for the process server, that is their job so there is no problem with that. I wish you good luck.