Of course nobody who posts on here looks at pornography and/or tries to hide it from employer, teacher, partner or parents, so any guidance is bound to be strictly theoretical. Having said that, I can think of a number of strategies that a person might use to hide any sort of material. It is a good idea to protect credit card, bank account records, and if you work from home, employment and work related information, particularly if your work involves protecting client confidentiality. In that latter case, I would use pro-level encryption and firewalling.
In fact, I would state that any individual has the right to their privacy, as long as they are not breaking the law. I think this point is very important, so I am emphasising it. I might add that a person who stores "xxx porn", "gay porn" and "tranny porn" is not necessarily "sick" at all. So I am not 100% sure about all this. You make him sound awfully bad.
Here we appear to be talking about a partner hiding (possibly not illegal) *censored* stuff from a non-tech-savvy partner who knows you don't have vast sums of money to spend on professional data recovery.
Only a fool would store any such material in plain sight. By that I mean as visible and playable document, picture or video files. For example "bank account details.doc" or "credit card numbers.xls" or "sexy cheerleaders.mpg" or whatever. One pretty obvious first step would be to place it in a password protected zip or rar archive, as has apparently been done. However, it may be that the errant husband was not too clever, because from what I can gather, although the archives were password protected, the contents filenames listing would still have been visible, leading to knowledge of the type of material being hidden. In other words, he had neglected to encrypt the filenames. It's no good passwording a zip file if Mom can see that it's full of files like hotbikini001.jpg, even if she cannot extract or view them. If, in addition, the zip or rar file's extension has been altered or deleted, a double click in Windows won't even open it. MomNEEDShelp, how did you know that this stuff was "teen porn"? It sounds like the "protection" was fairly basic if you (a) found the files (b) were able to tell what they contained.
So I would be searching for suspiciously large files with either no extension, or an unusual one. Maybe hidden files in a hidden partition. But I would not hold out a lot of hope of finding anything, especially if this guy could have had access to the computer since they were last viewed by you.
If I am not mistaken, EVERYTHING is stored somewhere on the hard drive, meaning even if they were cookies or temp files, they would still be somewhere retrievable. Am I wrong?
Files that have been deleted or placed in the recycle bin could well have been overwritten by other data. It is definitely not true that everything that ever happened on a computer is "there somewhere". Also, it is possible to set limits on temp and cookie storage space, so that when it becomes full, older stuff is automatically deleted. There are a number of such privacy settings that can be adjusted to make observation by others a difficult task.