All three cited contexts have significantly different meanings - which is to say that off one's feet doesn't actually have a single precise meaning. Context is everything...
1: The doctor told me to stay off my feet for a few days.
The doctor is advising the patient to take it easy, rest up, spend more time sitting down.
2: They were blown off their feet by the force of the explosion.
The explosive blast was so powerful that people nearby were propelled off the ground briefly (their feet actually lost contact with the ground for some amount of time).
3: Before Christmas, most salespeople are rushed off their feet.
The salespeople were so busy serving customers that they wouldn't have had time to sit and rest.
But all the above are perfectly common idiomatic usages (where the specific sense is strongly associated with the preceding verb - stay, blown, rushed). One more relatively common one that comes to mind is...
4: She survived by dreaming about being picked by a wealthy man who would sweep her off her feet and rescue her from her miserable life.
She hopes to meet a man who will really captivate / impress her.