I did a lot of research on strings and it seems that many people are using mono-filament aka fishing line. The problem is fishing line is measured in pound test while strings are measured in diameter. And once you've found the pound test fishing line you want, you need to find where you can buy it.
Some people might say its better to just buy strings from a music store, but what fun would that be. Besides, if you're going to making several Sq'Ukes, you'll need lots of string.
If you want to experiment for yourself, look at the D'Addario site http://stringtensionpro.com/. This site will calculate the tension given several parameters. My goal was to keep the strings approximately the same tension...5 lbs.
One interesting thing about strings is that the note is dependent on the tension of the string and the weight. If you look at a guitar, you'll notice the lower tones have strings that look like springs (even on classical guitars which are strung with nylon). These strings are actually wrapped in wire to make them heavier. There are many videos online showing how the strings are wrapped.
I experimented with trying to braid or twist 2 pieces of fishing line together. I even tried using a rope making technique simply to give the string more weight. This worked somewhat, the downside was that they didn't sit on the frets properly. The best idea is to get heavier gauge string.
Strings are a critical part of a ukulele because without them, you'd have a drum with a handle. I'm hoping to get some discussion going about different ideas for strings.