Folk-Roots or Alt-Country or Edge-Rock, there really isn't a way to categorize Wilco, so why bother when you can listen to them!
I got to listen to them live on Tuesday night at the Jubilee (the twin of Edmonton's Jubilee as Wilco mentioned after their opening band Califone did too). Lucky me!
Wilco proved that they can play amazing music generating huge sound on some of the more experimental numbers like Bull Black Nova from their most recent album to some sweet melody like on Jesus, Etc. which they let the audience sing until the middle of verse 2.