Got a Cobra 29 or 25' play with the TX mixer L18/L21 that long twin coil tank.
To develop "spurries" or harmonics, you just need to mix two signals together. RF or Audio. You can generate problems with simple overdrive of one signal.
You hear these events all the time on a typical CB - just listen to a local using an amp - not too hard to hear the "bandwidth" products - or even use a simple Heterodyne experiment thru two - single tone oscillators and just adjust the frequency of one so that it can "Beat" resonate to the other or move off resonance and you'll hear a pitch change in tone as a difference a generation of a Third - and even further tuning away, can generate a series of complex fundamentals.
You asked about Oscillation though, and much of that is thru design artifacts, improper matching of impedance and or power levels between stages making the output on one appear unbalanced to another.
Gain of the stage can also play a role -
You can also make a stage with such high gain, the part can place itself in a loop so it oscillates - so you need to correct the errant effect by neutralization - design a loop of a negative feedback path to correct the negative error
The "random" chance is also a part can self destruct from the parasitic oscillation - a frequency either higher or lower than the original frequency - due to mixing products. Or one part, or combination thereof, can work to make a "resonate tank" that is similar to a relaxation oscillator - self induced.
Much of the "spurious" effort is wasted heating and extra power consumption - but can still be seen
Even the use of a typical Power meter - a 2nd harmonic from the 1st - ADDS into the power present for the meter to "see".
In some cases, the 2nd harmonic or any order higher, adds their power to the meter - until the meters band width ability to detect the frequencies in it's band pass - exceed it's detectable bandwidth.
It's why Spectrum Analyzers are one of many preferred tools of the trade, a tech, engineer or designer can see the effects of saturation, clipping and distortion. It is then their job - to force the stage to produce more power into the band it's designed for, not wasted on extra frequencies not desired.