A couple of thoughts. And sorry this has happened for you, must be very stressful and difficult.
On hard discs, nothing is every 'erased' completely until the disk is full up and there is no more room, then the backup process will start to copy over the actual space occupied by old files, and they will be lost.
Unless your external disc is very full up, then if you are just backing up files over to it, then the chances are your old files will still be there, but with their file names changed so they don't appear in directory listings. That makes their space 'available' if needed. It is only needed when there isn't actually any 'free' space left on the hard drive.
There is software you can get which can retrieve these 'renamed' files and get them back for you. If you google 'recover deleted files' you will find a lot of information about software and processes which can do this.
http://is.gd/KaPVP7
Unfortunatelly, if you used Time Machine, the chances re it reformatted your hard drive. It depends on the kind of formatting it did as to whether you can get your data back? You can find out more about this here:
http://is.gd/6juYrr
There is a strange 'law' which says that until disaster strikes, then people assume disaster is only something that happens to someone else! Another 'law' states that unless your data exists in 3 different places, then it isn't truly secure. ie, the original copy, a backup copy, and another backup copy. Sounds over the top, until something terrible happens, then it seems common sense.
I hope you manage to recover the files ok. You might want to try one of the many 'data recovery' services, which can get data back off even hard discs that have been incinerated in fires ...
Barry