Literally, I take the socks off of me. I always have to remember this when dealing with articles of clothing on the body, whether wearing them, taking them off, putting them on.
I could also say "Jag tar av mina strumpor", but then It is not 100% sure that I take them off my own feet, someone could have borrowed my socks, e.g. my daughter, and I took them off her feet ...
Of the same reason that English does not say: 'My the socks'. When a noun is in the definite form, the definition can either be only the definite article (here plural -orna) or with a pronoun ('mina strumpor'), or some other determining word. But in this sentence: Jag tar av mig strumporna I suspect you mix up 'mig' which has to do with the verb, with 'mina' that definies the noun. We say "ta av sig", reflexive form, to show that it is I who take off my own socks on myself, where as English just say 'take off' and instead put the definition on the noun, as being 'my socks'. I hope this did not mix it up to much for you.
Can you translate this "I take the socks off"? If you take them off from another person?
Your English sentence is possible, but then you would have to change the Swedish sentence to: "Jag tar av strumporna" - and without 'mig' it becomes ambigous, if you mean your own socks or somebody elses, with a slight leaning to somebody elses, since we would prefer to use 'tar av mig' (reflexive verb-form) when referring to 'my own'
Can we put the (av) in the end of the sentence like in English? eg: I take my socks off