The thickness of the strings on a guitar are different. If I had the thickness of one type only, could I tune the guitar appropriately still? And how would it sound? Would it sound just bland? (adapting the nut as well)
Interesting concept, however, if you were aiming to tune it to conventional standard tuning you would run into a few problems. For example;
If you used only 1st E strings, the 2nd-6th strings would not have enough tension to produce the pitches contained in conventional standard tuning.
If you only used 6th E strings, the other strings would quite simply break if you tried to apply the tension necessary for standard tuning.
I think it is fair to say that tuning a guitar with strings of only one gauge to the standard tuning range is impossible.
If you really wanted to get the notes from standard tuning, you could try using lower gauge G strings. You could try tuning those strings as follows:
I supposed if you played the guitar tuned like that with those strings, it would sound extremely odd, like playing a guitar in Nashville tuning, but more mixed up and backwards sounding. The range of the guitar would be less, but you may get some nice chorus (the 1st and 6th strings will be producing the same note, for example).
Thinking about it, it would be fun to try out, but only if I was thoroughly willing to waste the £10 or so required to buy a load of the same strings.
Hope this helps! :)