Vacuum tube distortion mechanism
All the effects you mention are much faster than relevant to audio signals, so have nothing to do with audio distortion.

The dynamic characteristic of a triode makes it look sortof like a variable resistor with a variable voltage offset once you get to some minimum current level.  Both these are controlled by the grid voltage.  However, this is merely a first order approximation of what really happens.  The exact relationship from grid voltage to plate voltage with a fixed plate power supply and load resistor is non-linear.  You get more output change for the same grid voltage delta at high grid voltages than low ones near "cut off".

This non-linear function causes harmonics if not dealt with.  The usual way of dealing with this is to operate the tube over a part of its range where the relaltionship is not too non-linear, and to use negative feedback.  Usually you'd use a cathode resistor for some immediate negative feedback around a single stage, then some global negative feedback around most of the amplifier.

These techniques are effective enough in a well-designed tube amp to not be much of a issue.  The speaker will introduce considerably more distortion.  The main difference between tube and transistor amps is what happens when you overdrive them.  Tubes are more "soft" in getting to their maximum values.  The tops of too-large waveforms are not just hard clipped at some level, but "squashed" before being eventually limited.  This type of distortion is more pleasing to many people, especially if it's done symmetrically on the tops and bottoms of the waveforms.