Well, you wouldn't be able to make the runner as shown, since it is calling for 2 2/3 yds of fabric in total, and the only 1/4 yd fabric is calling for a straight quarter, not a fat quarter. In fact, after looking at it more closely, I see that the pattern is calling for several width of fabric strips.
This just doesn't look like a good option for these fabrics; however, I am sure there are some people on this forum who could suggest a pattern that would work for what you have :-)