Okoye was 19 when he was drafted 10th overall, the youngest player ever taken in the first round.
Orlovsky played in only one game in two seasons in Houston and did not complete a pass. He signed a three-year contract with Houston in March 2009, and was Matt Schaub's backup in 2010.
Anderson has played all five of his seasons in Houston, and caught 11 passes for 117 yards in 2010.
The team also announced Saturday that it had signed undrafted free agent Darius Morris, an offensive tackle out of Temple.
The Texans open training camp on Sunday. The cuts come the day after the team introduced cornerback Johnathan Joseph and safety Danieal Manning, two free-agent acquisitions brought in to help improve the league's worst pass defense.
New defensive coordinator Wade Phillips is implementing a 3-4 defensive alignment, and the Texans apparently thought the 6-foot-2, 315-pound Okoye wasn't a good fit for it. The former Louisville star disappointed after a strong rookie year, when he made 32 tackles, including 5 1-2 sacks.
Okoye had a career-high 44 tackles in 2010, including three sacks, but the Texans' defense ranked at or near the bottom of the league in virtually every defensive category. Houston used six of its eight draft picks on defensive players, and Phillips plans to use Shaun Cody and Earl Mitchell at nose tackle, leaving Okoye out of the mix.
Orlovsky worked with starting quarterback Matt Schaub and other teammates during the lockout.
But the Texans drafted North Carolina quarterback T.J. Yates in the fifth round, then re-signed Matt Leinart this week, making Orlovsky the odd man out on the depth chart. Orlovsky was a fifth-round pick by Detroit in 2005 and played 10 games in 2008, when the Lions finished 0-16.
Anderson was drafted by the Texans in the seventh round in 2006, out of Colorado State. He also returned punts and played on special teams in Houston.
Also gone from last year's roster are linebacker Zac Diles, who joined St. Louis, and punter Matt Turk, who agreed to terms with Jacksonville.
Houston is still trying to re-sign free agent fullback Vonta Leach, an All-Pro in 2010. The 6-foot, 255-pound Leach was the lead blocker for Arian Foster, the NFL's leading rusher in 2010 with 1,616 yards.