Airwolf/WMG

MD Helicopters is under Soviet mind-control and has been for a long time
How else does the Soviet Union get enough MD 500 Defender helicopters to export them?

The Soviet Union had a secret factory in the Urals that produced reverse-engineered imitation MD Helicopters
It's not like the Soviets cared that much about Intellectual Property.

Seasons 1-3 and Season 4 take place in (slightly) different continuities

 * This is the reason for the complete non-appearence of Caitlin (they never met her) as well as the "The FIRM"/The Company" difference.

Stringfellow Hawke is easily duped
Archangel could have had someone fly the Airwolf out of its lair anytime he wanted. But as long as Hawke could be talked into doing missions for him by letting him think he had the upper hand, why not?
 * Archangel says early on that his deal with Hawke is the only way the Firm can avoid red tape and political hot water while using Airwolf, possibly referencing the senator's summation at Red Star that developing weapons like Airwolf isn't in the Firm's job description. Zeus seems to have stopped caring when Airwolf 2 rolls off the assembly line, for all the good it did.