If you quit without notice and reapply after a few months can the company legally refuse to rehire you not telling you a reason why even though they have signs saying they're hiring now?

Yes. Each employer is free to decide who they will hire, as long as they don't discriminate against applicants based on race, color, religion, sex, national origin, disability, age (over 40) or pregnancy. There is no law that they must hire you back. Many, many companies have the policy of not rehiring people who quit without notice.