Adrian, I can help with part of your problem. The first thing you need to do is create Windows Live ID's for each of your Office Live email accounts. Start with "Log in with a different account" on the WLID log-in screen. Make one using each OL email address. There may be some additional work to do inside of OL, establishing passwords, hint questions, etc. if that's not already done. Make sure you can log into each account.
The next thing to do is link you WLID's. Again from the log-in screen, click on "Account" at the bottom of the screen. You will have to enter your password to open it. Now click on "Manage linked ID's." Add each email account to the list. When you finish, you will now get multiple ID's appearing in the log-in screen. You can save your email and password on your computer to make this all simpler.
Now, when you log into an email account, there will be a drop-down list in the upper right corner. This will give you access to all of your accounts from one log-in. As you said, I hope this is clear.
I am not sure, but there is a chance that this may also solve you Outlook problem. Good luck.