Hi Nathan,
I think the best way to learn sight-singing is a combination of playing the notes on a piano, associating intervals with bits of songs, and then testing yourself using games available online. Check http://www.Musictechteacher.com/musicquizzes.htm for lots of easy games. They're designed for kids, but they do help you to test your progress in a quick and simple way.
Also, remember that the 7th in "Twist and Shout" is a minor 7th, i.e. it's not the 7th of the major scale.
Here are some song references for intervals, and if you aren't familiar with these songs, there's a good list of them on www.earmaster.com:
Major 2nd: "God Save The Queen/My Country 'Tis Of Thee"-- the second and third pitches
Major 3rd: "Oh When The Saints Come Marching In"
Perfect 4th: "Amazing Grace"
Perfect 5th: "BaBa Black Sheep/Twinkle Twinkle Little Star/ABCD" -- the second and third pitches
Major 6th: "Hush Little Baby"
Major 7th: "Somewhere Over The Rainbow" -- the first and third pitches
Octave: "Somewhere Over The Rainbow"
Minor 2nd: "White Christmas"
Minor 3rd: "What Child Is This"
Tritone: "The Simpsons Theme"
Minor 6th: "Love Story Theme" -- the third and fourth pitches
Minor 7th: "Somewhere"
Hope this helps. Good luck!