It makes no difference. You do it exactly the same as on a straight quilt no matter where you are on the oval. You overlap the ends the width of your unfolded raw binding strip. The bias will help hug the curved edge. I did a circle and it was no problem.
Edited to add, I don't cut my ends on a diagonal. With bias, I straighten them out and then measure my overlap on the straight ends. then I sew on the diagonal and trim away the excess. So hopefully you have enough excess binding to cut them on the straight on the end.