What does the concept of "female strength" imply in Western culture,
as opposed to the more traditional concept of "male strength" (i.e.
big, fast, hard, powerful, efficient and other hard attributes)? Since
"strength" is almost always defined from a man's point of view, a
woman who exhibits traditionally male features is often perceived as
being "strong". But female strength has to be something other than a
woman acting like a man...right? Examples would be very welcome!

If the traditional view of male strength is physical and stoic, then
female strength would be more social, interactive and supportive. If
men are competetive and independent, then women would tend to be more
subtle and manipulative. Men would be apt to use a trial-and-error
approach to problem solving, women would be more intuitive. Men would
be more likely to try unconventional methods while women would be more
follow-the-rules in achieving goals.

The hand that rocks the cradle rules the world.
Behind every successful man is a strong/clever/intelligent woman.
    (Remember the joke about Hillary Clinton and the gas station attendant?)
The mothers of Ottoman rulers not only ruled the haram, they were
often the power behind the throne.

There must be more sayings and examples of strong women who did not
compete or succeed by stepping into the man's role  - as CEO,
commander (Joan of Arc) etc.

Then, of course, there is Lady MacBeth.

Antigone in the eponymous play by Sophocles is one embodiment of
female strength.  If you were doing non-traditional casting you
couldn't cast a man in that part.  She is stubborn and more loyal to
"what's right" than to rules of behaviour or the local hierarchy.  In
the Anouih translation greek to french to english this brute female
stubbornness is even more explicit:  "I am not here to argue with you
Creon, I am here to say 'no' to you and die".  She does, too.  Female
strength most always loses in the Western tradition. According to
Robert A. Johnson in "Femininity Lost and Regained" (ISBN
0-06-016271-6) Harper & Row, New York) it is completely the opposite
in the Hindu tradition, strong women win and are still beautiful.
However even such a paragon as Dropedi in the Mahabarata went to hell
at last, much to the sorrow of lots of girl readers.

But you asked for examples, and perhaps you'd like something a little
more contemporary than my Antigone.  Emma Goldman and Rosa Luxenburg
are at least starters and If I were making a list I would include
Sinead O'Connor.  Some say she's a nut case but so what.  You asked
for strong, not sane.  Another non-contemporary is Queen Margarethe
(or Margaret) of Denmark I, (not II).  She did what no king has ever
done, uniting the three scandinavian countries under one sovereign
(her).  The medieval scandinavian nobles were pretty rough stuff and
there were several assiniation attempts and betrayals that had to be
headed off quickly, but she lived in the midst of this stuff happy as
a clam and just loving her job.  She reformed a few other things too,
she was very effective.  Do you perhaps read Old Danish?  Neither do
I, but that where the best sources are.  Good Luck.

Ah, strong political roles for women? They can be very diverse:
Cleopatra
Elizabeth I
Margaret Thatcher
Indira Ghandi
Golda Meir
Hillary Clinton?