Display multiple clips in DaVinci Resolve 12
You are on The right track! There is not a specific effect to accomplish what you want to achieve.  

The only way (unless there is a 3rd party plugin, I don't know about) is to stack the 4 clips on separate tracks in the edit tab. Select one of them open the inspector (panel on the top right of the edit page) scale down and adjust the placement.  The video clip on the video track below should become visible. 

[Added by Michael Tiemann as a friendly amendment: In the panel where the scaling information is displayed, there are also parameters for the anchor point.  By default, images are scaled from the center, which means you have to add in X and Y offsets to get each clip going to each corner.  Instead, you can set the upper left anchor point to be the upper left corner of the video, the upper right to be the upper right, etc.  Then, when you scale, each video clip will retreat to its own corner.  If you want to animate this effect, you can have one clip expand from its corner and go fullscreen by scaling back to 100%, and you can return it to its corner by scaling down to 50%.]

Good luck.