If the cards used are green, you can use a green screen.
I personally am using Corel Video Studio pro X5.
In that software what you want can be done very easily.
It also does not matter what color the cards are, but it is a lot easier if the are stable like on a table or something.
Place the videos on the time line in an overlay track, and pin the corners to each respective corner of your video cards. The cards do not even have to be level, as in they can even be tilted.
I am kind of a newbie myself, but forced myself to learn Corels software as I produced a Wedding Montage/collage for their reception and made a video of their cerrimony. Both were done wonderfully using the corel software.
