Does EVERYBODY have either a Soprano, Alto, or Tenor voice?

No you are missing B, the lowest male parts. Most choral music is arranged for Soprano (sometimes broken down further into Soprano 1 & 2), Alto, Tenor (also sometimes Tenor 1 & 2), and B. The 1 parts are generally a higher range than the 2. There are other names for these parts as well that were used in older music from a few hundred years ago, including baritone (b), mezzosoprano (soprano 2 or alto), etc.