At the first level you need to compare cross sectional area of the 18" round duct with the cross sectional area of the four 8" oval ducts. There is a secondary effect of using the multiple smaller ducts because it exposes the air flow to more inside surface area which increases the pressure drop some but that can be compensated for by making the replacement duct area be larger than the original.
The cross sectional area of an 18" diameter duct is:
I do not know the shape of the 8" oval duct that you were considering but assuming that it is a standard ellipse shape like this:
We can see that the A dimension would be half of the 8" size and the B dimension would be half of the standard 2x4 wall stud width of 3.5"
If using four of the oval ducts the total area would be:
21.99 * 4 = 87.96 sq inches.
So to compare 254.45 from the large duct to the 87.96 from the four smaller ones you can see that only about a third of the required area is provided. So the answer would be no, this is not a suitable replacement.
Of course if the 8" oval duct has a slightly different shape this could affect the calculation some but I'd still say that it wouldn't be enough.
Here is a graphical comparison:
Update for Obround Ducting
The obround ducting available from one source is 3" by 8" in size (assuming the 8" specified by the original poster).
The cross sectional area of a duct this size:
So for the 3x8 size being considered it would take (254.45 / 22.06) = 11.53 ducts to be equivalent to the one 18" round duct!!!