Are u using World axis to move your object or Object axis. Latter can cause trouble while moving more than one object together if the object is already rotated.

Also scaling deformation of an object sometimes happens in maya if you attach or detach objects in groups. See if there is a "Transform" node is attached to any of your mesh objects in the outliner. If it is there remove it ( ungroup & delete ) and then delete history of the object.

I hope i'm close to the solution of your problem if not accurate. !!