CMH Controller described a confused air carrier routing event when area weather conditions required significant flight planning changes that eventually resulted in a failed hand off to ZID.

Narrative

Thunderstorms in area; although not directly impacting our airport at the time. For example; reroutes to ORD were going way south; and there was only one route. This weather made CD very complex; as we had an over abundance of notes on STOPS; SWAPS; CFRs; EDCT programs; AFP programs; etc. At one point I asked ZID flow if they could put in a reroute for an ORD aircraft; and the answer was; 'Yes; but it might be tomorrow before I get it in.' ZID Flow Control was down the tubes big time. During my position relief briefing; previous controller informed me that Air Carrier X was expecting a reroute from company; thus I was expecting a new strip at any time. Apparently the pilot of Air Carrier X didn't feel like waiting for the new flight plan; and told Ground Control that he'd depart on the old one; and work out his routing change with ZID. He then departed on the old flight plan. A new strip on Air Carrier X printed shortly after aircraft departed; and I saw FRC in the remarks. I told Ground Control & Local about it; not realizing the flight had departed. Local came over to me and compared the flight plans; and that's when I learned that the pilot had departed on the old flight plan and was maybe ten miles west of CMH. Being as the aircraft was already airborne; I performed a 'remove strips' on the new flight plan. At least I thought it was the new flight plan. It turned out to be the active flight plan! My actions resulted in Air Carrier X failing on hand off to ZID. I hurriedly put in the old flight plan; and got on the hand off line and informed Lytle Sector of my error; and that the new flight plan was now in the system. They accepted the hand off; and all appears to be okay. We rarely; if ever; have a Supervisor in our Tower Cab. That results in CD often being CS [supervisor] as well. During weather that is affecting our area; it would be nice to actually have the CS [supervisor] position staffed.