"I am not strong, even though I eat vegetables."
Translation:Nie jestem silna, choć jem warzywa.
Concerning the use of "ja" (yes, it means "I"):
"Ja nie jestem silna, choć jem warzywa" - I think it's OK (especially in spoken language), but it puts an emphasis on "Ja"="I";
"Nie jestem silna, choć ja jem warzywa", "Ja nie jestem silna, choć ja jem warzywa" - both are extremely weird and almost surely incorrect (not because of the word order -- if you would like to add "ja" that would be the reasonable places for it -- it just doesn't sound right...).
I will copy my answer from another discussion, rather for others as I think you're getting notifications anyway:
"Actually it's good that you capitalized "JA", because this is exactly how your sentence feels. Like a strong, rather strange emphasis. Even stranger, given the fact that the subject is the same in both clauses. If you want to use a pronoun, at least use it in the first clause (still redundant, but okay). But in the second one, when it's the same subject? No, that doesn't feel natural at all. Such answers are still accepted here and there, but I remove them when I see one.
Look at it like that: If "I" eat vegatables, then who else is supposed to be strong rather than "I"? Of course it's supposed to be me. Nothing else makes sense. Stating it explicitly doesn't make sense."
Same thing for this sentence. It's not like the fact that my brother eats vegetables could make me stronger, so if I am not strong, that's also clear that it's despite me not eating vegetables. It's just strange to put it there.