Spectral plot shows more notes than there really should be
Since the notes from a guitar are no pure sinusoids, you should expect to see some harmonics, even when analyzing the dry signal without effects. E.g., the note E is the perfect fifth of the note A, i.e., it is the second harmonic.

If you use distortion or modulation effects (chorus, flanger, and phaser) you get even more additional frequencies due to the non-linearity (distortion) or due to time-varying filtering (modulation effects).

So in sum there are three sources of additional frequency components different from the fundamental pitches:


harmonics (due to non-sinusoidal signal)
non-linearities (e.g., overdrive/distortion)
time-varying filtering (e.g., modulation effects)


And in your example you get all three of them.