I've got a couple. But best bet would be to upload a pic of the PC case so we could get a visual idea of what you are asking about.
1) An adhesive cement. Sold at various hardware stores. Most times it comes in a small tube. Putty like substance that you mush around and then place it to the back of the power strip and the case. It's permanent though, shit doesn't come apart.
2) Wire tie it somehow? If vertically maybe there are some holes you could wrap it through.
3) Take the putty I talked about and bond 2 fairly strong magnets to the back of the power strip. Boom!! if it is a magnetic case. If not just place 2 magnets on the outside of the case to "pinch" the case between them. I would recommend strong magnets as you don't want your power strip falling down.
That's about all I got...