I was just curious. The "trading deadline" was July 31. Yet, teams are still jockeying players around here in August. Are all of the players moving these days those that cleared waivers in August? I thought that might be the explanation. Otherwise, what sense is there to have a "trade deadline" in July?

Yes.
A player must clear waivers in order to be traded after the July 31 trading deadline.
Putting a player out on waivers is not risk-free. It has happened that a team, trying to block the Yankees or some Yankee equivalent from picking up a big name/big price veteran, has put in a claim and gotten stuck with a mega-contract.

I'm assuming that the 40-man expansion of rosters is still on, right? I think that after tomorrow, teams can add minor leaguers. It's also about that time that contending teams start renting players from the bottom feeders for the stretch run.

August 31 is the deadline for teams to acquire players who can be eligible to be on their playoff rosters. September 1 the roster expands from 25 to 40.