The vast majority of EEOC complaints end with a right to sue letter. The EEOC takes on only a very few cases to litigate itself on behalf of employees. Look for lawyers who concentrate their practice in litigating employment discrimination cases.
Federal law prohibits discrimination based on citizenship. As the company was losing money, needed to downsize, and laid off both citizens and noncitizens alike in the layoff, you'll likely have an extremely hard time making a case that you were fired illegally because of your citizenship.
As for the severance packages, whether you have a good case for illegal discrimination depends on the details of why the American employees got the severance and they did not. Did the company offer any explanation for that? Were the American employees in different positions, or were they union members and the foreign workers were not, or was there some other difference in their status that might explain the differing severence treatment? Those kinds of details are important.
You should also be prepared for one other hurdle. Your case would likely get tried to a jury. Many Americans resent foreigners taking jobs in this country believing that it takes away jobs from Americans, and given the difficult employment situation for a number of Americans after 2008 that resentment is still pretty acute among a number of people. So the jury is likely to start out without a lot of sympathy for foreign workers. You'd need to overcome any resentment of foreign workers to get the jury on your side.
Whether the case might proceed as a class action depends on whether all the foreign workers are similarly situated (which they may be with respect to the severence issue) and how many of them there are. How many foreign workers were laid off without severance? If there were just a handful then it would likely not be big enough for a class action, though the employees might still be able to jointly sue the employer. This is something to discuss with the lawyers you contact.