Employment Law Questions? Ask an Employment Lawyer.
Regrettably, there is no way for you to get the employment files unless and until you sue them, alleging some sort of discrimination and/or wrongful termination. You have really identified any facts to support that sort of claim here though. If you had no employment contract, specifically stating that you could only be terminated for cause, you can legally be terminated at any time, with or without cause...so the strength of the cause doesn't really matter legally.
If you are alleging discrimination, then the EEOC can obtain those files when they do their investigation.
As for your pay issues, if they are refusing you the pay stubs, you should file a complaint with your state's Department of Labor (called a wage claim). State that you are not being given evidence of your final pay, and you can't correctly determine if they paid you properly and so you want to file a wage claim since the employer isn't cooperating.
The employer would then have to provide that evidence, in defense of the allegation, to the DOL.
It appears that you had some sort of inquiry. Did you have some other question for me in relation to this subject?