So with Tractor Beam (TB) I know if your hit with the tb then you lose 1 agility and if it was a small ship your opponent gets to do a barrell roll or boost on your ship. Also that the boost or barrel roll dosen't count as action or manuever, and you can make them overlap obstacles but not ships. So my question is since the barrel roll or boost that your opponent can make you do is not an 'action or manuever', could they barrel roll or boost your ship off of the play area?

No

• A ship cannot barrel roll if it would overlap another ship or an obstacle token, or if the maneuver template would overlap an obstacle token.
• A ship cannot barrel roll if this would cause the ship to flee the battlefield.

• A ship cannot boost if it would overlap another ship or an obstacle token, or if the maneuver template would overlap an obstacle token.
• A ship cannot boost if this would cause the ship to flee the battlefield.

While TB allows an exception for obstacles, there's no such exception for fleeing the battlefield.

FAQ v411, p16. Boost and Barrel Roll specifically can't take you outside the play area, regardless of whether they're actions.