Hi Colin,
I am sure that there will be exceptions, but here are the most common usages for each of the three particles that you listed:
In general, 被is the default particle for forming passive sentences in modern colloquial Chinese.
For example:
我被他欺负了 (I was bullied by him)
午餐被他吃光了 (The lunch was eaten all up by him)
受 literally means "to receive." I would not use it to form passive sentences like you would with 被. Instead, 受 is often associated with certain objects, such as 受苦, 受难, 受气, 受害, respectively ("to receive bitter" = “to suffer (a hardship); "to receive difficulty" = "to suffer a calamity"; "to receive air/anger" = "to suffer mistreatment"; "to receive bad" = "to be a victim")
So I would use 受 mostly in "set phrases" or "fixed expressions," such as:
他大学时,因为家境贫困,常常受苦。When he was in college, because his family was poor, he often suffered hardship.
这艘船在太平洋受难了。 This ship suffered a mishap in the Pacific Ocean (e.g., it sank)
Finally, I would use 由 to indicate some sort of delegation of duty.
這件事由他來做最恰當。It is most appropriate for him to undertake this task.
这堂课由我来教就可以了。It is sufficient/good enough for me to teach this class (it is good enough to let me teach this class).
Again, there will always be exceptions but these are the most general rules I can think of. Hope this was helpful.