You won't find the ashOutXt.dll file but you should find what is called the avast plug-in.
I can't be of much practical help as I don't use any version of MS Outlook.
However in any case your installation doesn't seem to have completed correctly or the uninstall function would have worked.
Try a repair of avast. Add Remove programs, select 'avast! Anti-Virus,' click the Change/Remove button and scroll down to Repair, click next and follow.
If that doesn't work it would probably be best to do a clean reinstall.
Download the latest version of avast http://www.avast.com/eng/download-avast-home.html
and save it to your HDD, somewhere you can find it again. Use that when you reinstall.
Download the avast! Uninstall Utility, find it here
and save it to your HDD.
1. Now uninstall (using add remove programs, if you can't do that start from the next step), reboot.
2. run the avast! Uninstall Utility, reboot. If step 1 failed it may be necessary to run this from safe mode (as the avast self-defence module may be running), once complete reboot into normal mode.
3. install the latest version, reboot.