I'm sorry, but based on what you've described, those files may have been irrecoverably overwritten.

That "recovery software you found on the internet" may or may not have found the original physical locations of the files in question, however, those locations were overwritten by the files of the newly installed operating system. The recovery software just copied whatever it has found on those locations to your USB drive - but the contents of those "recovered" files are most likely junk, originally parts of some system file. They don't have any relation with your original, pre-format files, you can't recover your original data from them.

There are some professional data recovery firms that deal with cases like this; they may get back some of your data for $10000s.

Fully recovering data from an overwritten hard drive - I don't think anyone but the NSA can do that.