They can try, they will not be successful. Eventually they will be.

You did NOT get an eviction notice unless it is a legal document signed by a judge and issued by the court. Courts are not hearing eviction cases now.

What you probably got was a demand notice for rent with the threat of eviction to follow if you do not pay or vacate the premises within the stated amount of time. AKA the 'pay or quit' notice. That is NOT an eviction notice.

Depends on where you live. My tenant here in L.A. could skip rent for half a year before I have any recourse against him. Different places have different emergency rules on this.

WHERE?  There is no Federal law banning evictions.

You can appeal the unemployment decision.

Contact someone in your state about being evicted.

Unfortunately there are no uniform universal guidelines for handling the financial side of reacting to the virus pandemic. So we can't answer your question because you haven't said where you are living to be evicted from. Each State and city has its own rules on that. And those rules are most likely posted online. So I suggest you find your city's COVID-19 web pages and see what protection you have, if any, from eviction.

For example, both San Francisco and Oakland, CA have eviction protection regulations in place. But I've no clue about anywhere else.

You move out, obviously. There are charitable places that provide shelter, but where you're living now is obviously not one of them.

Why did you get denied for unemployment?Any chance of appealing?

It depends on were you live.  It is possible. In general you need to be evicted by  court in the US. States and cities have different rules.