This means that "Nem vagyok jól" so it has the same meaning, but in a separate way
I spotted 'yok' and remembered my Turkish. How many simularities are there between Hungarian and Turkish anyway?
There are some vocab similarities (mostly loan words in Hungarian from Turkish) and there are some superficial similarities in the grammar. They are pretty different though if you go any deeper than a superficial level.
The "yok" in "vagyok" actually has nothing to do with Turkish "yok". Turkish "yok" is "nincs" in Hungarian (would be spelled "ninç" in Turkish).
There are many, like elma=alma, var=van, and if you know some turkish, the grammar will be easier for you.
So, can anyone explain the word order? Is it O-S-V without the verb sometimes, or is it only in situations where they would say "I am ____" ?
The word order in Hungarian is very flexible and can take any permutation of S-O-V, but the neutral word order is SVO.
Usually personal pronouns can be omitted as they are implied by the verb (in this case, 'vagyok')
Are you a native speaker? Since I've studied I've been under the impression that the verb comes last in a "van" sentence, but any other sentence with a definite object has the verb come first.
Not quite. For example the sentence "I go to school" can be translated as "Megyek az iskolába", or "Iskolába megyek". Both are correct, but in the first the emphasis is on the action (I go), in the second is on the place I go.
I'd disagree with the 2nd example (iskolába megyek). In this case the emphasis is on the place (iskolába - to school). For example You see a kid with books in his/her hands, and You ask him/her where (s)he is going? (Hova mész?) Or You ask the kid "Are You going to the library?" (Könyvtárba mész?) and the kid answers, No, I'm going to school (Nem, iskolába megyek)
These are short simple sentences, this one doesn't even have an object. The verbs can be anywhere and even come first "van" and all others too.
Van egy tyúkom. - I have a hen.
Reggelente vagyok rosszul. - In the mornings I feel unwell.
The exact rules will be detailed later. One trick we often use is to move something up front to emphasize it. The sentence above does that with mornings. eg.
Egy tyúkom van - I have one hen. (emphasis on one)
Tyúkom van - What I have is a hen. (eg. when being asked do I have a hen or a rooster)
Yay! First sentence I could deduce the meaning of without looking at the translations!
Literally "rosszul vagyok" means "I am not well" and "beteg vagyok" means "I am sick".