Is it legal for an Ohio company to say they are not going to pay vacation time which has accrued if someone quits? Regardless of whether notice is given to the employer or not? This would be vacation pay, that accrues as an employee works.

Yes, it is perfectly legal. Ohio law does not require the payout of vacation time at termination.

How about accrued vacation in Indiana, is it required to be paid?

Although Indiana has no law making it mandatory to pay out vacation at termination, there have been court cases in which it has been ruled that the vacation is considered wages and therefore is due the employee.

If you are in Ohio, Ohio law applies to you, EVEN IF the employer is incorporated in Indiana.