It could be a couple of things.
First make sure you are using the 64-bit version of Python (or 32 bit ParaView, but we discontinued those a long time ago). You’ll have to hunt through the downloads page since their default Python download for windows is 32 bit. Based on your ‘not a valid win32 application’ error, I suspect this is the problem.
Then you need to set environment variables (you can set these in your shell before running python if you don’t want to set them globally):
PATH should contain C:\ParaView-4.4.0-Qt4-Windows-64bit\bin. You were trying to do this in Python with sys.path, but the dynamic loader needs it set before the application starts. You may also need the location of the .pyd files (I can’t remember… it has been a few years since I last did this).
PYTHONPATH should contain C:\ParaView-4.4.0-Qt4-Windows-64bit\lib\paraview-4.4\site-packages. You can set this one from inside Python with sys.path.
This should mean you can inport paraview or vtk in your system python assuming the version mismatch doesn’t break anything. In my experience all Python 2.7.X versions are compatible, so you should be fine.
cc: @allison.vacanti Here is another person who is working around the vector graphics thing…