Would it still be a sin to lie to protect innocent people or generally resist any sort of oppressor?

The jesuits used the concept of mental reservation specifically because of murderous oppression in england, deriving it from the fact that abraham told sarah to tell the egyptians that she was his sister -- she was indeed his half sister ("half" being the mentally reserved portion), but also his wife.

wide mental reservation (simply saying half a statement and thinking of a predicate that makes the spoken part true) has since been condemned (srsly, wide mental reservation is just lying), but mental reservation by equivocation is still acceptable.

Example: when the nazis come knocking, if you say to them "there's no jewish filth in this house", you have not lied (that is, spoken something which is at variance to what you believe to be true), given that you do not consider the jews in your attic to be filth, but you have indeed performed mental reservation by equivocation because the nazis equivocate jews with jewish filth.

Would it be wrong to violently resist?

no. I don't have prooftexts for just war or self defense off the top of my head, though, so you'll have to ask someone else if you're looking for scripture alone.