Is it normal for eye discharge to stink?

No. Eye discharge should not smell bad. It may represent a bacterial infection and you should call your doctor for advice.
Stinky eye stuff. It is now typical for eye discharge to smell. A significant smell could indicate a bacterial eye infection.
No. "Normal" eye discharge has no odor. If there is an odor it might reflect an infection of the eye. Other things with odor that might get into the eye are quickly flushed out. Any eye with an odor needs immediate evaluation.