The best way to achieve this, as far as I can see, is by creating a single image file (in Photoshop or GIMP or something) and then importing that into Premiere - unless, of course, you're animating all of the images in or something - then just moving/scaling on one 'clip' as opposed to trying to move and scale across a lot of different clips.
If you are animating the images in, nesting the video would be the best thing to do (as Shultc suggested) though the terminology in Premiere is a 'subsequence', not a 'composition'. To do this, select all of the clips, right click and go down to 'Make subsequence' - this will create a new sequence in your project that you can drop into your main sequence. Edit the content in the subsequence by loading it (double-click) as you would a normal sequence. Any changes you make will be reflected in the subsequence clip.
If you have After Effects, I'd suggest building this effect in there as it's far more useful for creating effects like this than Premiere is, though the process would be fairly similar, you'd just create a pre-composition with your collage in it, then edit (move/scale) the pre-comp in your main comp.