"I do not need them, I have you!"
Translation:אני לא צריך אותם, יש לי אותך!
The use of a direct object is considered to be technically incorrect but to not use it sounds wrong to most speakers of modern Israeli Hebrew. I guess most people who revived Hebrew took it as analogous to "ikh hob" in Yiddish or similar constructions in other languages
I am guessing you misspelled אותר and meant אותך?!
The difference is number. As you know, Hebrew distinguishes between אתה "you" when addressing one (male) person (את is the feminine form) and אתם "you" when addressing multiple people (אתן is for multiple women only).
So אותך is the object pronoun of אתה - singular "you" and אתכם is the object pronoun of אתם - plural "you".