take it on/off and put it on/off

Ah! Phrasal verbs! The foreign learner's delight. But you're talking about two types here - literal and metaphorical. The idea of putting on and taking off clothes is pretty literal - you put them on your body and take them off your body - and shouldn't create too many problems (I also teach foreign learners). But when it comes to the task, that's more metaphorical, and that's where the problems start.

There's not often a great logic to phrasal verbs, and the only real way for students to learn them is through exposure and use. Mind you, even when metaphorical, the particles often have common meanings, for example 'up' often means 'completely' - 'Come on, drink up', 'Tidy up' etc. But I'm sure you've got books which tell you that.

Hungarian itself has phrasal verbs - "meg" or "el" often correspond to "up" in English, giving a perfective, or sense of completion. Unfortunately, "put on clothes" in Hungarian is more like "dress up", and "dress up" more like "dress out", while "undress" is more like "take down" rather than "take off". The one that used to bug me was "post" a letter, in Hungarian is like "give up", but "Don't give up" translates word for word..
So try learning some Hungarian if you would understand the learner's plight. As for teaching phrasal verbs, with a monolingual class it's a good idea to mark up your own copy of the teaching materials with the translation and prick up ears when they start whispering Hungarian. My success rate for phrasal verbs was abysmally low but "ne adj fel!" "Making Sense of Phrasal Verbs" (Martin Shovel) is still my favorite.

@jayles - it's my theory that both Polish and German have phrasal verbs, and that German is a half-way house between Polish and English.

Polish has sixteen prefixes based on prepositions which are regularly put at the beginning of verbs. So, for example,we have the basic (perfective) verb form 'chodzić' - go (on foot).

Then we have wchodzić - enter, go in (w = in), wychodzić - go out (wy = out), przychodzić - come, arrive (przy = at), przechodzić - pass, go through (przez = through), etc.

And in German we have ausgeben and eingeben etc. Why I say German is in between Polish and English is that in Polish the preposition and verb are always together, in German they're sometimes together, in the infinitive for example, and sometimes separated, whereas in English they're always separated.

When I suggest this to my Polish students, they just look at me in bewilderment, but it's my theory, and I'm sticking to it.

@WW yes Polish is like Russian (apart from the script) ; your examples sound almost the same: ходить / входить / выходить / приходить; and the prefixes are inseparable - same in Latin/French/Spanish. However in Hungarian the particle is sometimes separable: "feladtam" = I gave up; "nem adtam fel" = I didn't give up.
(And maddeningly "elado" = for sale; "kiado" = for rent - so confusing! - and thus "eladtam" = I sold it; "nem adtam el" = I didn't sell it.

AFAIK only English can form the noun in two different ways with different meanings like "the lookout", "the outlook"; "an outbreak", "a breakout".

Jayles, yes I'm learning Hungarian, and it's not easy! But as you mentioned, my Hungarian husband often says "dress up" when he means get dressed. And other literally translated phrases. It might help to start thinking in his incorrect English, then translate literally to Hungarian, and voila, I'll be fluent!
We just discussed some phrasal verbs and the negation this week in HU class... Gives me a headache for sure!

So why does the Merriam-Webster just use this meaning of "put sth. off"? While it might not be a phrasal expression in your area, it seems to be used in parts of USA.

https://www.merriam-webster.com/dictionary/put%20off