Context: in order to repay a monetary debt, Fujioka Haruhi 藤岡ハルヒ has to pretend to be a boy at a high school host club, and to play the part she uses the pronoun ore 俺. Hearing her say this, the club president, Suou Tamaki 須王環, who instantly started acting like he's her father, says:
{onna no} ko ga "ore" nante ikemasen!! 女の子が「俺」なんていけません！！ Girls shouldn't [say] "ore!"
ikemasen - literally "can't go," translates as "shouldn't."
okaasan!!! Haruhi ga {kitanai} kotoba wo tsukau you~~!!! おかーさん！！！ハルヒが汚い言葉を使うよウーー！！！ Mother!!! Haruhi is using {dirty} words!!!
In Japanese, it's common for words that mean "mother," like okaasan お母さん, to be used to refer to one's wife, i.e. Tamaki is referring to his daughter's mother, not to his own mother.
okaasan? dare? お母さん？誰？ Mother? Who [is it]?
ore ka ne... nantonaku 俺かね･･･なんとなく Me, [I think]...
nantonaku - it just feels like it's so, used when you feel something is true for some reason or another, but you can't say exactly why you feel like that.
Although, in this case, it would be because Ootori Kyouya 鳳鏡夜 is the vice-president of the club.
