If he can remember the password then you can authorise that account on your computer's iTunes via the Store > Authorise This Computer menu option at the top of iTunes. If he can't remember the password then try http://iforgot.apple.com to get it reset
Do you have a copy of the songs anywhere, e.g. on an external drive, so that you can then add them to your iTunes library via File > Add To Library ?
If not then you might be able to redownload them (whether you can redownload music depends upon what country that you are in, and whether the tracks are still in your country's store) via the Purchased link under Quicklinks on the right-hand side of the iTunes store homepage (you will need to log out of your currently logged in account via the Store > Sign Out menu option, and sign in with the old account)
But redownloading an account's past purchases may tie your computer to that account for 90 days : http://support.apple.com/kb/HT4627 - so you won't be able to use iTunes Match, automatic downloads, or redownload past purchases on a different account until the 90 days have completed.
Or does your son use that account on a different computer so that you can try redownloading them on that computer and then copy them over to your computer ? On a Mac you can find where a song is stored on it by selecting it in the Music part of the library, control-clicking on it (right-click if using a PC), and select 'show in finder' ('show in explorer' on a PC) - you can then copy them to a flash drive or memory card, copy them onto your computer, and do File > Add To Library to add them to your iTunes library.
checked all the various Apple IDs and their accounts, and the different computers, plus checked purchases etc etc.
So I've found what there is to find. I think I've lost a few tracks but not too many.
Once upon a time you could redownload your purchases, but that has long gone.
Thanks for your thoughts and help.