Prepositions don't have to be part of a phrasal verb, in fact I would say most aren't. In this case, none of the prepositions have any special relation to the verb. They're all literal descriptors of the positions the subject goes through during the action.
Try to break up the sentence into the smallest chunks that make sense. Here: He fell. Yeah, that makes sense, that's true. Okay, where did he fall? Into the pool. What did he fall off of? He fell off the ledge. So now, put it together.
He fell off the ledge and into the pool.
You can leave out the "and" here, but it's still there for grammatical purposes. You can tell if you use three prepositions:
He fell off the ledge, through the air, and into the pool.
You can't leave out the "and" here, there's no way to use three prepositions without the conjunction. That means that there's no way to do it with two, either, and the "and" is still there, it's just not spoken.
Right and straight are both intensifiers, and don't really make sense to me here. There's not exactly an indirect way to fall off a ledge and into a pool.
I hope this helps.
Edit: A note to help distinguish between phrasal verbs and normal prepositional adverb phrases: phrasal verbs don't accept objects of the preposition, and they don't pair with prepositions in conjunction phrases.
The roof fell in. good
The roof fell in the house. not good
The roof fell in and onto the ground. not good
The roof fell in onto the ground. good
Does that help you see the difference a little better?
It appears to be a British vs American English issue. The Cambridge Guide to English Usage: Convention dictates that certain verbs and related words are followed by particular prepositions/particles. Words like compare/comparison take either with or to, and differ/different may take from, to or than, depending on the context, and which part of the English-speaking world you belong to. In Britain you fill in a form, whereas in the US you would express it as fill out. Note also the fact that, in American English, no preposition at all is needed with some verbs which do require one in British English. Compare:
British -- American
cater for a party -- cater a party
protest against the war -- protest the war
provide us with a plan -- provide us a plan
wrote to his MP -- wrote his Congressman
Best Answer
With true phrasal verbs like switch off and wake up, where the object falls depends on the 'weight' of the object. A 'heavy' object (one with many words) falls after the preposition/particle.†.
Putting the preposition/particle after such an object strands it too far from the verb, so both readers and hearers have to grope for the structure.
A medium-weight object may come before or after the preposition/particle.
But a very light object, like a single preposition, always comes before the preposition/particle.
†What you call off and up here varies among grammarians.