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?
All of the cars were stolen.
Both of the cars were stolen.
Half of the cars were stolen.
Several of the cars were stolen.
Some of the cars were stolen.
Few of the cars were stolen.
Most of the cars were stolen.
Many of the cars were stolen.
Or this:
All cars were stolen.
All the cars were stolen.
Both cars were stolen.
Both the cars were stolen.
Half cars were stolen.no
Half the cars were stolen.ok
Several the cars were stolen. no
Several cars were stolen.
Some the cars were stolen. no
Some cars where stolen.
Few the cars were stolen. no
Few cars were stolen.
Most the cars were stolen. no
Most cars were stolen.
Many the cars were stolen. no
Many cars were stolen.
{Several, some, few, most, many} do not accept another determiner. They must be used alone with the noun, or in a partitive construction with of.
Best Answer
In English, it's not incorrect to have two consecutive repeated words in a sentence, and one place you'll encounter that is a phrasal verb followed by a preposition.
For example:
However, sometimes the resulting wording reads a little awkwardly, so an author might try to rephrase the sentence to skirt the problem. Sometimes a comma might help improve readability: