Teams can still deal after the July 31st trade deadline passes. This MLBTR Glossary entry explains how trading in August works:
Teams have to pass players through revocable waivers to trade them after the July 31st deadline.
Players acquired after August 31st can't play in the postseason.
Teams will often put most of their players on waivers to determine interest, since they don't have to give up every player who's claimed.
Unclaimed players can be traded to any club in August.
Claimed players can be kept, traded or handed over to the claiming team (who would then pay the player's salary).
If only one team claims a player, he can only be dealt to that team.
If more than one team claims a player, he can only be traded to the team in his league with the worst record.
If a player's only claimed by teams in the other league, he can only be dealt to the team with the worst record.
Adam Dunn is one big-name player who has been dealt in August.