You seem to understand the meaning of the sentences quite well. The most suitable person to give you good, adequate translations of theses sentences in English is probably you yourself.
My impression is that you simply have to give up the idea that for one word in Language A (in all its variuos use-cases) there will be one specific word in Language B. There isn't. (Otherwise computer linguists weren't a thing.)
To help you, I try to express the meaning of these sentences in simple (basic) English. I think this should help you find good translations in more elaborate registers of speech. The German examples you quote are of rather high register: written language, theatre, radio (as opposed to street and youth language, informal chat etc.)
Er widersetzt sich dem Befehl.
He does not do what the superior person told him to do. This may be open resistance, or resistance in some hidden way.
Sie widersetzt sich seinem Kuss.
She behaves in a way making clear that she does not like to be kissed; or at least she pretends to be not liking it. Still the action is too weak to stop the kissing.
Das Volk widersetzt sich den Invasoren.
Members of the public do verious visible or invisible things to stop the invadors, or to make their life difficult.
Die Idee widersetzt sich der Logik.
The idea is not logical. It is contrary to logic. A thinking person cannot accept this idea. Note: etwas widersetzt sich der Logik is a very high register of speech, almost manieristic. Acceptable, but... well, a bit overdone.
Now it is your turn to find appropriate English phrases.
Later addition regarding "This ideas defies logic":
More normal ways to express this in standard German would be
Die Idee ist unlogisch
Der Idee fehlt es an Logik
Or if you want to use casual language (possible with good friends, or when offending your counterpart is no problem for you):
Die Idee ist Quatsch.
Or if you speak to superiors:
Ich verstehe die Idee nicht ganz.
Die Idee erschließt sich mir nicht.