Noleigator, I seem to be having a similar issue here.
I have tried migrating with the time machine disk, and it created a new user in my new Macbook Pro with Lion (came already installed). I ended up with 2 admins in my mac. I then copied all the files from the old user (the one that came with the migration) and pasted them on my new user. I tried to delete the old user in the "User and Groups", but it got stuck, always saying "deleting" and not doing a thing (checked the cpu, it was doing nothing).
I restarted the mac, and then noticed the other user was no longer there but the old files were still in the users folder. I had to delete them and thought the problem was solved (it was doing that thing of asking for the password from the begining).
Here is were it matches your problem: the individual files came indeed from the time machine and now they all have that "everyone - custom" in them.
(In my case, the folders have a "user" that doesn't seem to show up. I mean, it says "fetching..." and never does fetch the name. it has "read and write" privileges.)
If you change the custom to, for example, "read only", perhaps you will be able to delete it... at least I managed to without it asking for the password.
But of course, it is really time consuming to change this in every file.
I found here in this forum post
https://discussions.apple.com/thread/3199093?answerId=15844450022#15844450022
a possible solution for changing all the files with that "everyone-custom" into "read only".
I haven't tried it yet, but I intend to, and if it helps I will let you know!
here is the answer in that other forum post:
I had this issue too, but my file permissions were correct on my .Trash folder.
After a chat with a very helpful Apple Support rep the fix was to reset the permissions on the whole home folder.
Check the permissions on one of your offending files (Get Info) and if you see there are 2x 'everyone' permissions and one is set to 'custom' then you will have the same issue as me. If you change the 'custom' permission to something else you will find it will now delete.
I downloaded a small app called BatChmod and used this to batch process the permissions of my whole home folder. I suppose you could use chmod if you like ;-)
See pic below for the settings, and once run, log out and back in again.
Enjoy all your un-authenticated delete and move goodness!

I'll keep checking your post for possible solutions!