Umlauts on Sierra on English keyboard with Alt combo not working anymore for all Before Sierra:
Alt + O/A/U pressed then shortly afterwards O/A/U -> Ö/Ä/Ü

With Sierra:
Alt + O/A/U pressed then shortly afterwards O/A/U -> works only for ü
 with Alt + o -> ø, Alt + a -> å and pressing the key again leads only to normal letter
The default key combo in Sierra and older OS Xces on UK/US (physical and logical) keyboards to enter Umlauts is:

altu + a: ä
altu + o: ö
altu + u: ü  

You probably had a key modifier (like Karabiner) installed in your previous systems and remapped the key combo to get your non-default behavior.

At least Karabiner doesn't work in Sierra currently (as of Oct 2016) and you have to either wait for an update and/or use the old key combo again.