Just to add a bit to what has already been said: if you use sympySymPy, you can use symbols rather than strings which makes them mathematically useful.
import itertools
import sympy
x, y = sympy.symbols('x y')
somelist = [[x,y], [1,2,3], [4,5]]
somelist2 = [[1,2], [1,2,3], [4,5]]
for element in itertools.product(*somelist):
print element
About sympyAbout SymPy.