I know this was probably meant mostly in jest, but... to turn it into a learning opportunity: You are using the imperative mood, so I think you need to say "Ta av", not "Tar av". Next, "Ta av" wants an object, as in "take off from yourself". In English we usually omit this object, but in Norwegian I think you have to say "Ta av deg". To this you can now add "all your clothes", getting "Ta av deg alle dine klær" (or "Ta av deg alle klærne dine"). In English, this is literally "Take off from yourself all your clothes". But in English we would likely omit the object and say "Take off all your clothes". I don't think you can leave out the object in Norwegian, but instead would likely leave out the possessive "your", saying "Ta av deg alle klær" or "Ta av deg alle klærne". I'm just a beginner, so native-speakers please correct me if I got this wrong. (Or congratulate me if I got it right!)
In addition to what luke said, the "meg" also implies it's your own clothes in this case. "Jeg tar av deg klærne" would mean "I am taking your(singular) clothes off".
You could also say "Jeg tar av meg klærne dine", meaning you're using somebody else's clothes and taking them off.
What is the purpose of "meg" in this sentence?
"Klær" is already plural. So, "klærne" is "the clothes". To signify ownership, I would write "klærne mine" = "my clothes". I saw, in another comment, that the possessive pronoun can be omitted - so I'm okay there.
So, does that mean the sentence literally says "I'm taking the clothes off me / I'm taking off the clothes (that are on me)"?
Does the sentence lack meaning if it is just "Jeg tar av klærne"?
It's really saying "I'm taking from myself the clothes". "av meg" in the sentence is "from me" or "from myself", it's not describing the ownership of the clothes like we do in English when saying "I'm taking off my clothes". I think the fact that "av meg" sounds so similar to "off my" may lead some people to misunderstand the individual word meanings.
I too am wondering about the real purpose of "meg" here. Even though "from" is not listed (in "tips and notes") as a meaning for "av", I am thinking it might be useful to think of "tar av" as "take from", or "take off of", so that it is more obvious that an object is required. In that case, a literal translation would be "I am taking off of myself the clothes". So it seems to me that "meg" here is not really indicating possession, but is the reflexive object "myself". In that case, the given translation "I am taking my clothes off" is rather poor, as the English "my" is definitely indicating possession. In other words, the English sentence "I am taking my clothes off" does not indicate who the clothes are being removed from, it only indicates that the clothes belong to me. On the other hand, the Norwegian does not indicate who owns the clothes, it only indicates that I am taking them off of myself. In English, it would be admittedly awkward to say "I am taking off of myself my clothes", and we would just say "I am taking my clothes off" and the usual implication is that that I am taking them off of myself. In Norwegian, it appears that they are saying "I am taking the clothes off of myself", and the usual implication is that the clothes are mine...? Perhaps this is because "tar av" requires an object, so it's easier to leave out "mine" rather than "meg"? And to be fully unambiguous you would say "Jeg tar av meg klærne mine". So, although both the Norwegian and English here are what would normally be said, it may be useful to realize that "meg" here does not indicate possession, the way "my" does in English.
As I recall from formal grammar lessons (a long time ago), proper English does not like separating a prepositional verb (taking) from its preposition (off), so the best translation should really be "I am taking off my clothes." Certain English teachers of my youth were quite strict about this with their red pens, which is probably why I remember it now.
However, common usage doesn't recognize this rule, so this comment is only useful for people who like grammar minutia (or dl folks who want to be grammatically perfect ;).
Because literally, the translation is closer to "I take the clothes off me". The fact that the clothes belong to me is implied, but not actually there in the grammar, whereas the opposite is true in the English sentence, where the fact that the clothes belong to me is explicitly there in the grammar, but the fact that it's my body that they're being removed from is implied.