Hey Laura, I would say they are more formal, but that is not to say that "because of" is informal. I think "because of" can be either, but "Due to" and "owing to" sometimes sound more elegant or gentle, depending on the context. Often in an official setting, we use the other two to deliver a message more politely - "my mother had to leave the wedding early due to an emergency" might be preferable to "my mother had to leave the wedding early because of an emergency" which is still polite, but less elegant you could say. I'd say the difference though is very subtle, and some may actually disagree with me on this.
I think best think of it as different ways of saying the same thing - so that you can vary your language and not repeat the same phrase over and over.
Also Andrew is correct - "due to" does not have to follow the verb "to be" e.g. she left due to an emergency