Can someone give some good context and scenarios for using these? Not only when to use them, but when NOT to use them as well. I know あげる is kind of the most common, but I'm just not sure of the nuances between them.
Usually involves the transfer of a physical object from one person to another of equal (or sometimes lower) status.
Can function as あげる, but in modern Japanese it comes with a formal ring and often involves something given as a favor for someone of lower status. Beyond this, its alternate uses include "assign" as in "assign homework", as well as "give" in connection with abstract concepts, such as influence or impressions.
子供におやつを与える (can replace with あげる)
宿題を与える ("assign homework", note this also goes from higher to lower status)
影響を与える ("exert influence", abstract)
いい印象を与える ("give a good impression", also abstract)
Limited to giving something special (a privilege, a prize, etc) to someone of lower status. Closer to the English "award", "grant", or "bestow" than "give".
勲章を授ける ("award a medal")
知恵を授ける ("bestow wisdom")
Definitions and example sentences taken from the 大辞泉 definitions for あげる, 与える, and 授ける.