Since a while Microsoft is making this a bit easier by including the logs of the managed apps via the Company Portal in Android, a quick troubleshooting tip.
So when going in the Company Portal for Android to the three dots in the upper right corner and click Settings. Here you are not only to configure verbose logging (enabled by default) but also able to Send data. Clicking on this button will allow you to send a diagnostic report with the following files attached to an email.
Opening the ZIP file of the Outlook app will give you the logs of the app
Opening the com.microsoft.office.outlook_X.log file will give you lots of information about the Outlook app and how it is acting on the Android device in combination with Microsoft Intune.
If you have issues with the Outlook app for Android or iOS, be sure to create an in-app support case! This is a really nice way of getting support for the app and more logs are available for the support team.