Do you mean that if there are strong external fields then one would have an inconservation of momentum and so the collisions are not anymore elastic?
I read that kinetic gas theory is applicable only if the ideal gas is in thermodynamical equilibrium. Do the particles in a plasma all have the same temperature (electrons and ions)? I read that electrons are generally in near thermal equilibrium but positive ions are never in thermodynamical equilibrium and neutral gas molecules may or may not be in thermal equilibrium. Why?
as you correctly said, kinetic gas theory is valid if the ideal gas approximation applies, which means that particles can exchange energy and momentum only through collisions, either elastic or inelastic. However, in a plasma you will have charge carriers that can also exchange energy and momentum via electric and magnetic fields and this makes things more complicated.
Thermodynamicla equilibrium does not really influence kinetic gas theory, you can build distribution functions even if the particles are not in TD equilibrium. However, if they are, they follow the Maxwell-Boltzmann statistics, which is fairly easy to treat mathematically and can usually be handled analytically.
You can have different situations in plasma, there are thermal plasmas, which are in TD equilibrium, there are plasmas in which the electrons are in TD equilibrium with other electrons but not with the neutrals or ions and the other way around. If you deposit energy into a gas with ns pulsed fields or high frequent fields, the electrons take up the energy more efficiently, since the photons of the EM field are dominantly interacting with electrons. Furthermore, their mobility is larger due to their small mass. Hence, they can follow the oscillations of the field more easily and will, therefore, be heated most efficiently. If you don't have many collisions between electrons and ions or neutrals (for example, because you have strong anistropic E or B fields) getting into TD equilibrium is very difficult and/or takes a long time.