Oval shaped faces and curly hair can go in with the long curly hair on the sides while having it fairly short on top but not too much, see for example kit Harrington aka ‘Jon Snow’ from the popular TV series Game of Thrones. Even if you don’t have the curls required to emulate Snow, a wavy hair pattern with slight curls would do the trick. Wavy and curly hair patterns look good when styled messy as it gives it a more natural look.
Now for the ones with the square face, there is the popular undercut which is everywhere these days. With more volume on top it could be parted on either side, that’s your choice!!
For more classy hairstyles, check out http://www.zuleb.com/