One common algorithm to perform a shuffle is the Fisher-Yates shuffle. This generates uniformly distributed permutations.
To implement on a Delphi TStrings
object you can use this:
procedure Shuffle(Strings: TStrings);
var
i: Integer;
begin
for i := Strings.Count-1 downto 1 do
Strings.Exchange(i, Random(i+1));
end;
Now, whilst in theory this will generate uniformly distributed permutations, the actual performance depends heavily on the quality of the random number generator. This is discussed in Knuth's Art of Computer Programming, volume 2, section 3.4.2, Algorithm P.
Further reading:
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