The second の is a nominalizing の.
It turns the phrase 「すっごいレンジの音がしてる」 into a noun so the grammar 「Nが気になる」 can be used to mean "N is on one's mind" or a similar meaning.
Another example of this usage of の is:
(I) dislike playing video games.
This ～の～の roughly translates to "such things like ～ and ～", and it's a way to list two or more things with a certain negative feeling. It often implies the listed items are unimportant, meaningless and/or annoying, just as when you'd use "told to do this or that". ～だの～だの is similar and often interchangeable with this ～の～の. (～だの～だの can be used with nouns, ...