How can I recover a deleted file on Android?
Is there a way to recover deleted files on Android phones without using standard USB storage recovery tools?
First off, from a practicality standpoint I do not think there is a way to do this. Especially if the data was on internal storage. If the data was on an SD Card you could try googling for data recovery software or something along those lines and then mount the sd card and try searching it. But most software out there isn't made for sd cards.
Is your phone rooted? If so you should be creating backups with NAND at least every other week, I usually do them more often than that. Also you can use Titanium Backup to backup apps and system data. Neither of these will backup your SD card though. For that I just copy all contents from my sd card to a computer before a major change.
Check out the link below for more info, keep in mind I wrote that guide based on the Evo, but still it applies to almost any Android phone.