You can now delete the offending files from iCloud/iTunes and use your newly created AAC files instead.
If you've received "purchased" items from anyone, even if these items are DRM-free, the original purchaser's Apple ID is stored in the file which you can check by requesting "Get Info" for the file in iTunes. An alternative is to use one of Doug's AppleScripts (£1.64 - install into iTunes) and run this script to see all Apple ID's from all files in your entire iTunes library (it will create and populate new playlists by either the iTune's purchaser's name or I.D.).
So for example, you have some MP3 files you downloaded from a torrent or received from a friend (let's assume you own the CD so having an MP3 version is not a legal issue). If those MP3 files are considered "purchased" from Apple Store, then you are required to enter the Apple ID credentials for each of these items in order to download a new copy from the Apple Store. That's why it's asking for multiple logins during iCloud restore and when you "skip" each one, you'll eventually see your own Apple ID. By skipping these "unknown" Apple ID's, there does not seem to be a downside, since presumably you still have the originals in your iTunes library. If you were to provide the correct passwords, these items would be downloaded from the Apple Store otherwise.
To prevent this happening find and remove these various "purchased" files that contain the unknown Apple IDs. If there is no copyright issue, you could do a "Create an AAC version" in iTunes which makes an identical copy minus the "purchased" status and Apple ID (if you don't already have these items in your iTunes library, then this is a moot point since you wouldn't have been able to re-download these "unauthorized" files from the Apple Store anyway).
You can now delete the offending files from iCloud/iTunes and use your newly created AAC files instead.