In a couple of days (hopefully after you have seen this reply), I shall move this topic to the Data Forensics forum, as it really belongs there.
Your question begs a lot of other questions, answers to some of which might not be in the public domain. But the really important point is that Eraser is best understood not so much as a stand-alone application but as one of a variety of tools and techniques with which users can protect their privacy and security. So the effectiveness of the defence against an adversary (in this case a forensic specialist, who will use specialist software tools) will depend on the whole defensive system, rather than Eraser in isolation.
To give one obvious (but also frequently encountered) example, it is no good claiming that Eraser is ineffective if you have failed to identify and erase all copies of the target data on your machine. You can expect that forensic specialists will know where to look for traces that have been left behind in this way; experience suggests that most users are unaware that such traces exist, much less how to remove them.
That said, some things are known with at least a reasonable degree of certainty. Experimental work on modern mechanical hard drives has shown that a single overwriting pass is sufficient to put the data that is overwritten beyond practical recovery; artefacts will remain, but they cannot be reliably used to reconstruct the original data.
Thus, when an overwriting program such as Eraser writes to the whole disk area used by a target file and the associated file table entries, that file (including any metadata the file or file system might contain) is completely and permanently destroyed. I am not aware of any published claim that this is not the case. Also, with modern drives, a single pass erase is as effective as a 35 pass erase; forensic analysis will therefore typically focus on the security weaknesses of the target system rather than attempt to recover erased data.
It is my personal belief that, because traces are so hard to find and remove, an ordinary private user will find it virtually impossible to secure his or her data against sustained expert forensic examination, other (possibly) than by encrypting all sensitive data. The ordinary user can however reasonably easily protect himself or herself against the more commonly encountered computer security threats, and that Eraser is a useful and effective tool in this latter context.
I hope that this response is helpful. It is not a full answer to your question; such an answer would probably fill a book!
David