I have installed the Outlook app on an iPad and iPhone with the latest iOS8. I have an IMAP email account but the app is unable to connect to it.
The native iOS email client on both devices will connect to this IMAP account OK. But when I enter the same settings in the Outlook app's Advanced Settings entry screen (which are the server, etc. settings provided by my ISP), it comes back with a message that it cannot connect.
I note that the entry screens in the current Outlook app differ from those shown in the relevant Office365 knowledge base article here:
https://support.office.com/en-au/article/Set-up-email-on-iPhone-iPad-or-iPod-Touch-b2de2161-cc1d-49ef-9ef9-81acd1c8e234?ui=en-US&rs=en-AU&ad=AU&fromAR=1#BKMK_IMAPorPOP
The article shows screenshots with options to select/deselect SSL and enter port numbers. These options don't appear when I use the IMAP setup option in Outlook for iOS.
Note that when iOS makes the connection, it does not use SSL or ask for port numbers. These parameters can only be accessed via the advanced account settings for the account AFTER the device has added the account.
I should add that I also have an Exchange email account, which can be set up in both the iOS email client and the iOS Outlook app without difficulty.
And also that the Outlook app exhibits the same behaviour on Android - i.e. the Android email client lets me set up the IMAP account but Outlook for Android is unable to connect.