5g nano's aren't touch screens but I get what you are describing...if I hit the enter button when a song is playing it gives me the option to have shuffle off, shuffle songs, or shuffle albums. I have checked this as well and it states shuffle is off but it isn't. Ever setting on the iPod shows that shuffle is off but as soon as I go to my song list or start playing a song, it's in shuffle.
If anyone is still having issues with this, I've figured it out. I, like most, must've turned this on accidentally and was sure I needed a new iPod until now.
1) Play a song in whatever playlist on your iPod.
2) When the song is playing, tap the screen and slide it to the left. This should reveal the screen to the right.
3) On this next screen, 3 symbols will appear in the center of the screen, a round "repeat" symbol, a "genius" symbol shaped sort of like a star, and and a "shuffle" symbol that resembles a soft "x".
4) Tap on the 3rd "x" symbol to turn off shuffle.