Buildings and trees were splintered and blown about, closing some highways. Most are now cleared. I ran into one still closed in northern Georgia today. You could check the states' DOT web sites for closures that might affect your route.
Tuscaloosa will be rebuilding for months, but most places saw damage in narrow swaths of 1/10 or 2/10 mile width. Unless a place you wanted to stay got hit, I think you will see no adverse effects on your trip.
What Fred said. You'll mostly be crossing tornado tracks; don't tarry, unless you want to volunteer for a day to help with the cleanup, and you won't be a load on the system.
We just got power back last night (98.5 hours without electricity, but who's counting?
Nearest bad damage is about 7 miles north of home -- trees down, sometimes in yards or garages, in some cases across houses. West part of the county got hammered, but again, it's 1/2 to 1 mile wide, 60 miles long, total devastation; go a quarter mile off track, and there may be a few limbs down, a couple shingles missing, but everything else is normal.
Two things to watch out for right now: crap on roads (wood chips, bark, some glass, etc.), and branches cut off close to the edge of the road. You can tell the road crews were in a hurry -- sometimes the branches are cut off outside the pavement, sometimes 3-6" over the pavement.
Also, don't expect available or cheap motel rooms near the damaged areas. With hundreds of displaced families, they need the rooms more than you do.