Hello and welcome to JustAnswer.
Unfortunately, as an at will employee you can be terminated at any time for any reason (including a bad one or none at all, unless the reason is discriminatory) with or without prior notice.
However, in order for your employer to successfully contest your unemployment benefits, your employer needs to be able to prove that you were terminated 'for cause' and not through no fault of your own.
If you file for unemployment benefits, your employer will have to inform EDD of the reasons for your termination in order to attempt to deny you benefits.
Regardless, you should apply for unemployment benefits, which you can do so online here:
If you believe that you have been discriminated against based on a protected characteristic (such as race, gender, national origin, ethnicity, sex, or age) you should file a complaint against your employer with the Department of Fair Employment and Housing.
You can file a complaint using the instructions available here:http://dfeh.ca.gov/Complaints_eCompProc.htm