Does anyone know how much STR is Equal to one weapon attack?

Actually, the OP needs to take the partial derivative with respect to weapon attack and divide it by the partial derivative with respect to STR to get his desired ratio.

∂(Range) / ∂(W.Atk)
∂(Range) / ∂(STR)

= ∂(STR) / ∂(W.Atk)

∂[c/100*(4*STR+DEX)*(W.Atk)] / ∂(W.Atk)
∂[c/100*(4*STR+DEX)*(W.Atk)] / ∂(STR)

c/100*(4*STR+DEX)
c/100*4*(W.Atk)

(4*STR+DEX)
4*WAtk

Oh look. All the constants drop out anyways.

Now try it with the actual damage formula.

range = c / 100 * (4*floor[str*(1+%str)] + floor[dex*(1+%dex)]) * floor[w.atk*(1+%w.atk)]

If you assume the various variables are continuous, and remove the floors, it takes care of most of the problem, and you end up with a similar result. But of course it won't be perfectly accurate cause MS doesn't have continuous damage ranges.