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.
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".