Connotations of different "to give"
给 is the most common one and the equivalent to give in modern Chinese. 

And we do not use the single character 施. It is usually in words like 施舍， 施予 etc. 
Don't know where you see it meaning "waving banner" or "to spread". It just means normal to give in some words. However, this character have several means other than "give", which can be only identified by the word or context.

Also 予 is not used alone. "a looming shuttle" ??? I've no idea about this. Common words including 予: ～以 赐～ 赋～ 给～ . Note: sometimes its meaning is an abstraction of "give", and can be translated as "grant".

Last one, 赏, when it is a verb, the most precise translation maybe award, meaning grant someone his/her reward, and usually given by his/her superiors. For example, giving some gold to a war hero from his monarch.