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I don't know if volume 6 happens before or after the war games since volume 7 starts with them discussing the results of the war games.
Sword Oratoria 6 starts in the part between DanMachi 5 and 6 and lasts until the first part of DanMachi where Bell fights with Hyakinthos at the Hibachitei, as the rest of the Loki Familia head out for Melen right after
I've looked at the timeline and the way that the synopsis explains the time skips ( a day later, few days later, a while later etc) it's really hard to see what's happening when, or if it was even possible for that stuff to happen while the events of Danmachi are going on.
Synopses are a summary of what happens in the volume, it's not there to compare events with DanMachi. If you're having trouble, try finding events that happen in both volumes and work from there
After Bell comes back to the surface, they'd have to been in town for over a week and a half for Aiz to he at the ball and train Bell but the synopsis of 6 says Aiz wanted to see Bell the day after he returned to the surface but didn't know where he lived, then Loki announces the trip to Melen the next night. So basically she announces a trip almost exactly a week before it happens and then skips a week ahead?
As I mentioned above, Sword Oratoria 6 ends before the God's banquet takes place (the night of the incident at the Hibachitei to be exact), so it's perfectly possible for them to return in time for it. The epilogue of Sword Oratoria 6 happens the day after the banquet in the evening