I addressed some of the issues you raised in my article here:
www.psaudio.com
Psychoacoustics is more complicated than just odd and even order harmonics, because each harmonic has its own character. The sensitivity to distortion is also frequency dependent. In general, the sensitivity is much higher for high frequency signals than for frequencies from the mid-bass down. Some odd order harmonics sound objectionable because they are dissonant, and the brain will notice a very low level of such harmonics. What Jean Hiraga found in his experiments more than 30 years ago is that generally, each harmonic is masked by the harmonic lower down. Therefore, if the 4th is at a higher level than the 5th, for example, the high one will have less effect. SET amplifiers do not generate euphonic distortion per se, but the high levels of second and third harmonics serve to mask the higher ones. Second and third order harmonics are generally well tolerated, because musical instruments also generate a lot of these harmonics. Adding these harmonics to the fundamental causes what listeners describe as a " muddling effect", but if you add a dissonant harmonic, such as the 7th, even at a very low level, listeners will find it highly unpleasant.
Early transistor amplifiers did add mainly odd order harmonics, and this might be a function of high negative feedback with inadequate open loop gain. Intermodulation distortion is another subject, and this distortion is all dissonant.
Is it possible to design solid state amplifiers that have a "pleasant" harmonic spectrum while avoiding IMD ? Absolutely. You just need to know what you are doing. Equally, it is possible to design tube amplifiers that have objectionable harmonic spectra, although you would need to try hard.