When doing your own studies, it might help to use the right terminology. A prepositional phrase is a preposition (in, on, at...) and the words which follow it (a complement). eg: "The coffee was spilt on the carpet under the sofa in the living room." There are 3 prepositional phrases here: 1) on the carpet 2) under the sofa 3) in the living room You are referring to a phrasal verb. These consist of a verb + a prepositional or adverbial particle or both eg: "I had to cool down the coffee before I could drink it" 'Cool down' is the phrasal verb. Hopefully this clarification will help when looking up information (look up is also a phrasal verb)

To best understand a preposition, always think of it in terms of its physical meaning. Almost all of them have a physical meaning. For example, in "The cat jumped OFF the table" "off" expresses the fact that the cat jumped so that it would no longer be ON the table. Here's the secret to mastering phrases like the ones you mentioned. Every time you learn a new phrase, match it up with a mental picture that is just as physically vivid as a cat jumping off of a table. For example, suppose you see the sentence "the accused man hired an attorney to get off". Here, "off" is used in the sense of "away", as in "the cat ran OFF into the forest". So, the accused man wants to escape something, like the cat running into the forest. The thing he wants to escape is jail. Create a mental image of the accused man running (getting) OFF from jail and associate that image in your mind with "get off". He wants to get off, running away from jail. Do something similar with all such phrases. Gradually they will seem logical to you and you won't need to memorize anything.

I think you should consider refining your objective. Learning ‘phrasal verbs’ as a general objective doesn’t seem logical to me. Many of them are informal, regional, related to a subculture or specific to certain fields. With zero effort, I could give you examples that only a minority of even high level native English speakers would know. I learn new ones all the time. My general advice would be to really think about what kind of English you want to learn and then just expose yourself to authentic content of that type. Not only will that teach you phrasal verbs, it will improve much more important things! The exception to this advice is if your goal is to pass a test, because ‘Test English’ isn’t used authentically. In that case, find a teacher who knows what’s on the test you need to take.

Phrasal verbs can be really challenging, with the same phrasal verb having many different meanings. For example 'pick up' has at least 10 different meanings! One good way to really understand these phrases is my watching or listening to authentic material such as podcasts, series or movies as these phrases are used a lot by native speakers. Hope this helps :)

I recommend private tuition, in person or via video call, with a great teacher who can teach you every meaning when they introduce you to a new phrase, and every kind of phrase to convey any given meaning. Also, I recommend using Google, typing things like "get off definition" and "get off synonyms" and "get off antonyms" and "get off etymology" so you can really deeply understand any word or phrase you're learning. Wiktionary is also a great resource for learning the many meanings and etymology theories of any given word in any common language.