"(Of) different size" or "(of) different sizes"?

I think it depends on how many of the property are associated with the object. Whether you use plural form for the property can also depend on whether you use "of" or "with"

• two pipes of different weight.
• two pipes with different weights.
• three containers of different volume.

A pipe has many dimensions, for example: length, diameter and wall-thickness. So if you use a more general term like size, you may be saying that a plurality of dimensions may differ.

• Two pipes of different size.
• Two pipes with different sizes.
• Two pipes of different diameter.

The Futurama example is a bit different because the phrase "a length of wire" can be used as a noun. For example one can say "let me show you some of the different heaps of sand I use". So "different lengths of wire" could have the same meaning as "different pieces of wire" - they might differ more in diameter or hue rather than in length.

Two pipes with different diameters.

Clearly, there are two diameters because the diameters are different.

The same applies to the radii, but you more normally talk in terms of diameters of pipes than radii. (On those occasions when you do use radius in connection with a pipe, it tends to be the radius of the bend in the pipe rather than half the diameter of the pipe.)