There are apparently 79 moons orbiting Jupiter. Let's assume they are all numbered 1 - 79.
"Moons two through 78" means all the moons from number 2 up to and including number 78. This is an idiomatic use of the word "through" which means "up to and including a particular point in an ordered sequence". It is apparently North American in origin, but I have heard it used in British English.
"Extend my sympathies" is an idiomatic phrase which means to offer one's sympathies to someone.
The meaning of your quotation is meant to be humorous (obviously - it is in a comedy show). The humour is in the comparison that being a "middle child" (ie a child in a family of at least 3 siblings where they are neither the youngest nor the oldest sibling) is like being any of the moons except the first to be discovered (number 1, the "oldest") and the latest (number 79, the "youngest"). The speaker states that, as a middle child, his grandfather never learned his name, and the inference is that nobody will care about any of the moons except the first and last to be discovered.