If this just started, Yahoo is revamping its whole site. No one is exactly thrilled with it.
Can you log in on the computer? Yahoo just got around to messing with the mobile site.
If you can log in on the computer - uncheck "keep me logged in" It really means what it says - it is extremely hard to log out at all if that is checked. The menus disappear.
If your browser on the phone allows it - set the browser as a "desktop" and don't use Yahoo's app.
If you do get to log in - I'd delete the Yahoo app, make sure its cache is clear and try reinstalling it.