Hi and welcome to the forum.
Firstly, use the drive the deleted files are on the absolute minimum possible. In fact, only run a file recovery program on that drive.
Once a file is deleted, the header is removed; the body of the file is left behind, but the space it occupies is free to be overwritten by a new file. So that is why "don't use the drive" is important.
A possibly important factor is the way Avast deletes files. I don't know how it does. But if it is a standard delete, like you'd do in Windows explorer ( I hope it is) it will just remove the header and not the body.
Try (using the Undelete program) to open one of these files. As suggested in the programs' FAQ's, copy the potentially recoverable file to another drive before opening it. It's possible the undelete program has given the file that extension, which according to Lord Almighty Google, belongs to "free backup fixit". (Sound familiar? Got this program on board?)
Another program you could try is Recuva, by Piriform, (makers of Ccleaner). Install it on the C drive, then use it to scan the drive concerned. I know that it is straightforward to restore restorable JPG's/JPEG's with this program. Oncew again, restore them somewhere else, not the disk/partition they are to be read from.
There is a lot to be said about "unable to scan this file" reports. Basically, most of the time these files are not a threat and don't need any action beyond investigating the reason. But lets deal with the recovery first.
There is also stuff to be said about NOT deleting anything from the scan result, but moving it to the quarantine, in ordser that it can be restored later if needed. Hopefully you'll get away with this without losing the photos you've deleted, and it will cost nothing more that a bit of a lesson.