I'm looking for other expressions that describe "overwhelming force" as applied to the "shock and awe" American military doctrine or different kinds of asymmetric warfare.
Trivial sentence:
The empire attacked the rebel base with __________ (overwhelming force?).
Best Answer
The first thing that came to mind to fill the blank in your example sentence was:
“ … with all its might.”
However, that phrase would probably be overstating the actual/literal extent of the attack and even so overstated, it doesn’t necessarily imply, as “overwhelming” does, that the power of the attacking force disproportionately exceeded that of the force being attacked.
Granted, your use of "empire” and “rebel [base]” in the example sentence would probably lead one to assume that “all the might” of an Empire would be more than enough to defeat/overwhelm “all the might” of a rebel base. As you say yourself, however, your example is not only just an example, but a trivial one at that.
All that to try to say that without the “clues” of “empire” and “rebel base,” attacking “with all its might” does not guarantee that the defender’s might is not equal to or even greater than that of the attacker.
I do, however, think that replacing “force” with the noun sense of “might” would be a good first step in finding a suitable synonym for “overwhelming force” and that combining "might" with the complete/thorough/extreme sense of “crushing” could overcome the problems with “all its might”:
Here are two example uses of “crushing might” that seem to me to be synonymous, or nearly so, with “overwhelming force”: