Your initial instinct that take a hit is equivalent to taking a hard blow or damage is right. It took some digging, but I found the corresponding definition in the Oxford Dictionary:
noun
a verbal attack:
I think people will try to take a hit at my credibility
So to figuratively take a hit means that one is being hit by some sort of non-physical attack, usually in the form of a verbal barb. Although this definition doesn't mention it, this phrase is not particular to a verbal attack. Searching for "take a hit" leads to many news articles which refer to the economy "taking a hit"--as long as the object is taking some sort of damage.
The other meaning you found, regarding inhaling via the nose, refers to drug use. Thus people talk about taking bong hits, or a hit of marijuana.
Best Answer
They seem grammatically correct but the first and third are awkward. Better: