Puig, 28, hit .267 with 23 home runs and 63 RBIs with the Dodgers. The Reds traded for him on Dec. 21.
Casali, 30, hit .293 with four home runs and 16 RBIs in 52 games last season as a backup to starter Tucker Barnhart for the Reds. He joined the team on May 31 after the Reds purchased his contract from the Tampa Bay Rays. He made an immediate impact, hitting .407 in his first 11 games.
After missing all of the 2017 season, DeSclafani, 28, returned to the mound in 2018 and was 7-8 with a 4.93 ERA in 21 starts.
Lorenzen, 27, was 4-2 with a 3.11 ERA in 45 appearances. He made three starts.
The Reds acquired Roark from the Washington Nationals in a trade for Tanner Rainey in December. Roark, 32, was 64-54 with a 3.59 ERA in six seasons with the Nationals. He started 141 games and made 31 relief appearances.
The Reds did not reach a deal with the one other arbitration-eligible player, pitcher Alex Wood, before Friday’s deadline.