Thank you for the information and your question. I will assume by the facts that you provided that you never received any money from this expense report. If that is not the case, let me know, since there might be additional information I can provide to you.
As for your resignation, unless you have a contract that requires that you and the employer owe the other party any notice prior to terminating the employment relationship, then you can resign just as you have suggested and with no notice. You don't have to give a reason for your termination, just as your employer never needs to give a reason.
In regards XXXXX XXXXX accrued unused vacation pay, since there is no Ohio or Federal law that requires that an employer offer any vacation pay, the employer can set the policies for, among other things, the payment of unused vacation pay at the end of the employment relationship. That said, the employer's policy must be clearly stated in written policy or contract. Meaning that the policy must specifically state that they will not payout unused vacation pay upon separation in order to not have to. If their policy is silent, then they must pay it and if they don't, you could file a wage
claim or file small claims court suit.
Please let me know if you need any clarification. I would be glad to assist you further if I can.