Cruz was 1-2 with a 4.75 ERA in 41 2/3 innings for the RedHawks. It's his second stint with the Astros this year.
"Cruz got sent down then did a tremendous job and got better and better and better as the year went on," manager Bo Porter said.
Martinez spent most of the year with Double-A Corpus Christi before being promoted to Oklahoma City in mid-August. At the two levels combined, he went 14-4 with a 2.57 ERA in 140 1/3 innings over 29 appearances (21 starts).
The plan is for Martinez to be used in long relief and for Cruz to make spot relief appearances.
Laird batted .277 with 16 home runs and a club-leading 79 RBIs for Oklahoma City.
"We wanted to get a right-handed bat off the bench," Porter said. "He provides us with that right-handed bat."
Paredes hit .287 with 21 doubles and 16 stolen bases, appearing at shortstop (20 games), third base (20), second base (3) and in the outfield (35).
"You look at the season that Paredes put together," Porter said. "He's obviously a guy that has conquered Triple-A. He's done everything that a person can do there. We're going to continue to give him an opportunity here."
Paredes is in his fourth stint with the Astros this season. The three other callups are in their second stint.
Willie Bans is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.