...does Halo Wars run on?

I'd be willing to bet it's an in-house engine built specifically for Halo Wars. 

Well the control scheme was constructed using the Age of Mythology Engine.
The rest, like Sir_Ragnarok said, was probably done using an in-house engine.

Thanks for responding.

It's tough because a lot of games don't have this sort of information released.  If a big-time engine like Unreal 3 is used for a game, that's usually publicized, but unless the engine has a significant clout around it (the Oblivion/Fallout Gamebryo engine, for example), then you're not likely to hear anything about it.

Halo Wars uses Havok engine which is used for example in Halo 2, Halo 3, MotorStorm (PS3), Saints Row 1, Saints Row 2, Stuntman: Ignition, Test Drive Unlimited and X-Men: The Official Game according to the Havok website and also according to the Havok icon in those game packages.

"Halo Wars uses Havok engine which is used for example in Halo 2, Halo 3, MotorStorm (PS3), Saints Row 1, Saints Row 2, Stuntman: Ignition, Test Drive Unlimited and X-Men: The Official Game according to the Havok website and also according to the Havok icon in those game packages."

Havok is middleware i.e. one part of a game engine.