Oduya has played one game since returning from an ankle injury sustained Jan. 17.
"Health was an issue, but we had all the medical records and he's healthy now," Nill said. "He would have played tonight if he wasn't getting traded, so that wasn't an issue."
In 37 games this season, Oduya has seven points (one goal, six assists). He has 180 points (36 goals, 144 assists) in 783 regular-season games during 11 seasons with the Stars, New Jersey Devils, Atlanta Thrashers/Winnipeg Jets and Chicago Blackhawks.
Oduya has 28 points (six goals, 22 assists) in 102 Stanley Cup Playoff games.
The Washington Capitals selected Oduya in the seventh round (No. 221) of the 2001 NHL Draft.
McNeill was the No. 18 pick of the 2011 NHL Draft by Chicago. The 24-year-old center has played one NHL game. He has 28 points (six goals, 22 assists) in 58 games with Rockford of the American Hockey League this season and will join Texas of the AHL.
"Sometimes a change of scenery's good for somebody, so he's going to come here," Nill said. "It's a great opportunity for him. He'll add some depth to us and we'll see where it goes."