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You Cannot. The Aircrafts were just there for Display in the Airport, to make them Stand out or Something. Besides the Helicopters, They are not Drivable, Proberly Because they Don't have an Interior Inside, So In Short, no, they Cannot not be Stolen. The Only Plane that was "Enterable" in the GTA IV Era, was Ray Bulgarin's Ghawar.
The Ghawar Cannot be Stolen either Because the Cockpit's Interior wasn't Seen Clearly and that you Couldn't get inside Because after you kill Bulgarin's Men and eventually Bulgarin himself, Bulgarin Sets off a Grenade Just as he dies. Prompting Luis to Sky-Jump off the Plane, Resulting in the Plane in being Blown up, losing your Opportunity to Steal it.
Even after you kill Bulgarin's Men, When Bulgarin Comes out of the Cockpit threatening to Blow up the Plane with a live Grenade, even if you try to enter the Cockpit and Refuse to Kill Bulgarin, a Cutscene will appear and Luis will Kill Bulgarin. This is Prove that the Cockpit isn't "Enterable" nor is it Drivable to the Player. According to GTA Wiki, The Interior of the Plane is Only Seen During the Final-Mission: "Departure Time"; it is actually Smaller than it appears on the Outside and has a total of eleven chairs. The Cockpit Can be seen if the Player looks Closely when Ray emerges with a Grenade, although it is Rather Nondescript. There are twenty-four Windows Inside the Plane, all of which are Bulletproof.
During Departure Time, the Plane Doesn't actually move, as it Simply hovers in Place until the Russians are Killed and Ray exits the Cockpit.
Only During the Final-Mission: "Departure Time!" and the Ending Credits is the Ghawar actually Seen. The Only time the Ghawar is actually Seen in Gameplay is in the Mission: "Departure Time!" It is not Seen Outside of that Mission as it is not in the Airport in Multiplayer either. And as I Previously Stated in the Mission: Departure Time!", this Plane Cannot be Stolen because you have to Kill Bulgarin.
In the GTA IV Era, Helicopters were the Only Aircrafts you Could Pilot. (CW Included).
Rockstar Games Stated that Piloting the Planes around Liberty City and the State of Alderney wasn't very Spacious and Decided to use the Planes in the next GTA Installment: "GTA V".
It is Proberly not Possible to Pilot a Plane in Chinatown Wars either. As Seen in the Trailer, Screenshots and the GTA IV Easter Egg Poster in Funland at Firefly Island, Planes will Return and will be Pilotable in the next GTA Installment: GTA V as it will be in San Andreas as you Could Pilot Planes in San Andreas.
Until then, Unless you want to Steal and Pilot a Plane that badly, Steal One in either GTA III or San Andreas.