I have just installed nginx on Ubuntu 14.04 using the command
sudo apt-get install nginx
Now, when I open my browser and type in the address
It looks like by default they are set to go to stdout and stderr.
lrwxrwxrwx 1 root root 11 Apr 27 2016 access.log -> /dev/stdout lrwxrwxrwx 1 root root 11 Apr 27 2016 error.log -> /dev/stderr
So you can remove the symlinks and should be fine.
rm -f /var/log/nginx/*