Here is how to change the display language for Microsoft's online, consumer services: How to change the display language used for Outlook.com (the e-mail service and the calendar) How to change the ...
By following the above steps, you can activate the spellchecking feature in Outlook online for different languages. But you have to restart your browser every time you change the language for ...
You might want to double-check what language Outlook is set to since it uses MS Word for writing. For instance, many terms are spelled somewhat differently in US English and UK English.