Automatic spell check and Autocorrect not working

If your version of Outlook is different from the version of Word or when Word is not installed at all, some features will not be enabled including the automatic (background) spell checker and AutoCorrect.

In order for these features to work, Word and Outlook must be the same version.

Manual spell check and check before sending

The manual spell check feature will work even though Word is not installed and can be accessed via the keyboard shortcut F7 or in the Ribbon via;

• tab Review tab-> button Spelling & Grammar

To prevent yourself from sending out messages before checking them, you can also force Outlook to run a spell check when you press Send;

• File-> Options-> section Mail-> option: Always check spelling before sending

You only have "semi-automatic" spell check support
with a standalone version of Outlook.

Other features not available with standalone Outlook

For an overview of features not available when Word is not installed or not from the same version as Outlook see;

• Outlook 2013 features that use Word 2013

This also still applies to later versions of Outlook.

Workaround (use at own risk!)

A quick and dirty workaround would be to create an empty file called WINWORD.EXE and place it in the same directory as OUTLOOK.EXE. This will reinstate most of the missing features as these features aren't actually missing from the installation (Outlook only checks if WINWORD.EXE is there).

Important!
Note that this workaround isn't supported though and might lead to crashes if Outlook actually does make Word specific calls. This workaround could also be in breach with the Microsoft License Terms of Office/Outlook which (broadly) states;

You may not work around any technical restrictions or limitations in the software.

For these 2 reasons, I do not recommend using this workaround in a production environment but it might come in handy for some testing environments.