I plan to read TWGOK manga, especially the chapters that weren't animated (between Season 2 and Season 3). Which chapters do I need to read?
The first two seasons of the anime adapted everything from the beginning, and made it through Nagase's arc. Nagase's arc ends in chapter 41. Chapter 42 is an extra chapter, and 43 is the beginning of Tsukiyo's arc. From there until the start of season 3, the only parts that have been adapted are chapters 54-55 in the first OVA, and Tenri's arc (chapters 57-64; 56 is another extra chapter) in the second OVA. Season 3 animates the Goddesses arc, which begins chapter 114. Season 3 of the anime ends with chapter 189 of the manga. As of February 2014 this is everything that has been animated (unless you count the Magical☆Star Kanon 100% OVA which loosely adapts the corresponding spin-off manga chapters).
Hence, the minimum amount of reading to get all the main story arcs would be chapters 43-53, 65-113, and continuing from chapter 190. However, if you don't want to miss any of the extra content, I'd strongly suggest reading everything from the beginning. The story has a lot of bonus material and extra chapters that were never adapted, and many of the running jokes originate in those chapters.