Eli's gender is held ambiguous, especially in the movie (played by girl, dubbed by a boy). Oskar talks about Eli to strangers as "she" and his "girlfriend". Reasons for this behind the cut.
As you can read in the whited out section in
inveinted's
stats, Eli - short for Elias - is in fact a castrated boy. Most people assume from what Eli wears and how he looks like that he's a girl, and he usually doesn't bother to correct them until the issue is directly adressed. Oskar knows all of this and at the end of book and movie doesn't really care about it anymore. In camp he goes for what is easiest for Eli, hence what doesn't provoke questions or would draw attention to Eli. That's why he introduces him as his "girlfriend" and will, unless he knows you know better, adress Eli as "she". There may be a time when he changes this, but as long as he is relatively new in camp he goes for what he thinks is safer for them.
EDIT:
First slip occured when Oskar thought Graham kidnapped Eli. He referred to Eli as "he/him" towards Serifar and Graham It was my fault because I forgot but I HAVE A GOOD EXCUSE because Oskar was really worked up