Hello, I recently got laid off and my question is can I get unemployment benefits with either the social security number I work with or the itin number I report my taxes. Since I am undocumanted to work in the USA.

This is one opinion from a California Legal Aid society in their question and answer section. Other states may handle it differently but this approach makes sense to me.

"6. As an undocumented worker, can I collect unemployment insurance?
No.
To collect unemployment insurance, workers must be both “able to work” and “available for work”. The California Employment Development Department (EDD), the agency that decides who has the right to unemployment insurance, has determined that undocumented workers are not, 'available for work,' because they are not legally eligible for work. Therefore,undocumented workers normally cannot collect unemployment insurance. "

How do you have a social security number if you are not documented? (Illegal)