I think of a 'Sonic' screwdriver as a corruption of 'Psionic' screwdriver.
Like the 'Psychic Paper' it's a Do-What-I-Mean tool.
I guess it's probably both, Psionic control of a Sonic effect.
I do believe that it although it has "settings" (possibly a myriad of them), like the one to cut/uncut barbed wire (but very few, if any, which work well with wood), it
has been shown to "do what the wielder is thinking it ought to do". Inside the Tesselector (or whatever it was called), I think is an example of that behaviour.
It is somewhat a "machina ex deus", as it were. Mind you, Light Sabres can be made "solid and unburning" and could be alikened to a wooden staff that could be leant upon, or an unbreakable lever. But I think the magic of the Light Sabre is mostly in the mind of the Force User. (Certainly it was so in the old D6s Star Wars RPG, not sure if that's translated to the D20 variant that I've never played.)
I'm sure that you could "Sonic" the Sabre to disrupt it (stop it working, or mangle its internals to make it more dangerous, for either the wielded-against or the wielder). OTOH we know that the Screwdriver is not itself made of indestructible Unobtainium/Handwavium alloy[1], and even when not physically damaged (for example, one half finds itself left inside a sky-shark) there are times (often crucial ones, though never
utterly crucial) that the circuits/workings/whatever can overload from feedback or something else. As such, a carefully timed (possibly pre-emptive[2]) slash, or a Force Throw in a boomarang arc, could leave you with the distinct advantage[3].
However, I do know
one thing. With the advantage of Elite Stormtrooper Training, you probably need only possess a particularly viciously sharp slice of mango to prevail against the guys in white. I've always imagined that the body armour is reactive body armour, manufactured inside out by accident. You're better off wearing a leather jerkin, in such a gun-fight...
(Also I think you know (even if just in you heart) the answer to the old dilemma... What happens if Imperial Stormtroopers fight Enterprise Redshirts..? Answer: The Stormtroopers all miss, but the Redshirts die anyway.)
[1] Hmmm... I wonder if the Doctor could make a Sonic shell out of Dalekanium alloy? Or might the peculiar energies in that cause Problems (TM).
[2] If you're not worried about accumulating Dark Side Points
[3] Insofar as leaving the Doctor without a plan, without a weapon and without a hope of success
ever gives you the advantage...