There are in fact many songs which would not fit into 3-note per string scale, or for that matter, any scale.
As piiperi comments, scales are reference points. In music, a scale helps you know which notes to play in a certain key. However, melodies (or chords, harmonies, etc.) are not limited to using notes in the key. Songwriters will often "borrow" pitches from another key to expand the feel of the song. These are broadly referred to as "accidentals."
These are especially common in minor keys, for which there are three basic scales.
Perhaps you have only learned major and natural minor scales. I would assume so as you seem unfamiliar with pitches out of three note scales.
Here are examples in A minor.
As you may notice, these scales do not all contain the same notes, despite being the same key. In fact, some notes are out of key. Songs will use these accidentals and many others regularly. It is also important to remember that one song is not limited to using one scale or key. Many modulations may occur.
Since you mentioned trying to dictate for guitar, I will also point out that rock and metal have a particular fondness for breaking outside of conventional scales, as with Jazz.
As for training your ears, I'd look less into trying to transcribe set songs and more into practicing hearing intervals. That very well can work, but I've found practicing specific techniques is more effective. Ear training is a difficult task. In universities, multiple levels of courses are devoted to "Aural Skills."
Sites such as this one give excercises for Ear Training.
If you want to just learn by picking out the melody on your instrument, I'd suggest doing so with pop songs, lullabies, and Christian worship music if you're new to this skill. These may not be your preferred genres, but they have simpler melodies to better learn before progressing toward more complex genres.
*The melodic minor changes notes depending on whether you are ascending or descending the scale.