How can I fix this scaling issue I have? I'm trying to scale the cube to be the size of the house.. but this happens. 
https://youtu.be/1nITnqzOprI

Is there a way to solve this? 

Edit:
Scaling the X axis only deforms the cube. I'd like to make the cube the same width and length as the house. 

Edit: The only way I can get what I want is if I extrude and then merge the vertices. Which is a bit longer solution.
I think your mesh is not aligned with its own object's local axes.. (you may have reoriented the cube in Edit Mode). So the Local axes are aligned to Global axes, but the mesh isn't, it wouldn't make any difference whether you transform in Local or Global. It's probably quickest to start with a new cube. 

But you could select its top face, and CtrlAltSpace create a Custom Orientation from it, checking 'Use after Creation' and then transform the object in that space, SXX,SYY, etc. 

You could even reoirient the cube's local axes to one of its faces, by snapping a helper cube to one of its faces,CtrlJ, joining the object to the helper, and deleting the helper in Edit Mode.. but in this case, that would be silly.