Right now there are large American states which have 50 times more Coronavirus cases in ratio/proportion than others, with hundreds of cases close to a thousand, and there are even small states where cases are zero or near to zero. Do American states have the power to close their borders from other states in a health emergency, is there a workaround to apply this, or can even the federal government give this power temporarily to states or something?
US Constitutional law generally recognizes the right of freedom of movement, e.g. in Corfield v. Coryell, 6 Fed. Cas. 546, Crandall v. Nevada, 73 U.S. 35, Paul v. Virginia, 75 U.S. 168. The more recent case Saenz v. Roe, 526 U.S. 489 affirms the position that restricting the "right to travel violates the Equal Protection Clause absent a compelling governmental interest", and one of the specific rights subsumed under the right to travel is "the right to enter and leave another State".
The "compelling governmental interest" is a reference to standard of judicial review known as strict scrutiny, where a law that restricts a fundamental right (the right to travel) is required for a "compelling state interest", is "narrowly tailored" to that purpose, and is the "least restrictive means".
It is highly likely that each state has a statute that grants broad powers to the governor in case of a state of emergency. Such an order would then have to be scrutinized strictly, with respect to the narrow tailoring and least restrictive aspects of the question. We would then have to analyze the specifics of the case and order.