How to deal with repeated resubmissions of a bad paper (as a reviewer)?

This type of repeated submission of junk is something that I truly hate, but also don't know any good way of dealing with. The problem is that the same freedom that supports novel science also leaves room for this type of "publication-shopping." In essence: any more unified method of "disapproving" junk papers, to prevent them from wasting everybody's time, will also work against highly novel papers that are meeting resistance from entrenched communities---see, for example, the decades-long fight Barbara McClintock faced in getting her work on gene regulation accepted.

We are thus left with the current and default system, in which each publication judges independently, and in which reviewers face frustrating situations like the one you describe. My recommendation, then, is simply to judge the paper on its merits, of which it has little. The biggest key strike is the self-plagiarism: once you've discovered that, the rest doesn't really matter, because self-plagiarism is an offense worth rejecting a paper over in and of itself.

I would recommend informing the editor, along with informing the editor about the history of the paper. They may then either judge whether to speedily reject the paper (and possibly initiate proceedings against the authors for the self-plagiarism), or whether to ask you to formally write this assessment as a review.

If it still doesn't cut it, reject, again. In your comments say that you saw the paper before, and have rejected it.

Let the editor know in more detail what you think.

That the paper has been lightly revised a dozen times doesn't make it good, according to what you state.

Your question raises two issues, one of which is merely annoying, but the other concerns a possible breach of ethics. I think it's helpful to consider those two issues separately.

Regarding the fact that the paper is of subpar quality, there is nothing you can or need to do other than to reject the paper. The author is within his/her rights to write a junk paper and submit it to as many journals or conferences as he or she wishes. If he/she eventually finds a venue that will accept it, that is probably not a reputable venue and no one will pay it any attention, so I don't see it as anything to lose sleep over.

The self-plagiarism issue is more serious. From your question it sounds like you are starting to ask yourself whether additional action is warranted beyond merely rejecting the paper, on account of what you perceive as unethical behavior by the paper's author. Indeed, I can see that being the case based on your description, though it's hard to know for sure without knowing the extent of the self-plagiarism. One natural idea in this case is to contact someone from the author's institution (department chair, colleagues, ethics committee...) to alert them of his/her behavior. A complication here is that as a reviewer you are likely bound by confidentiality to the journals that asked you to do the reviews. (Although arguably the unethical behavior may be cause for rescinding that promise of confidentiality, but that's a tricky argument that I would try to refrain from making.) So, if I were considering such a step I would first of all contact the editors of all four journals/conferences, tell them what I am contemplating doing and explicitly ask their permission to contact the author's institution.

Alternatively, if you prefer not to get so involved in the story by taking such action (which would possibly involve you losing your anonymity and making yourself an enemy, who despite being in an unproductive stage of his/her career may still exert some influence over your field), you can email the four editors together, tell them the details of the story and put in their hands the decision whether to contact the author's institution or take further action. Of course, they may decide to do nothing.

Finally, I'll add that the sort of self-plagiarism you're describing sounds more pathetic than outrageous to me, and would probably be perceived by most people as a minor ethical infraction at worst. Trying to do something to prevent such behavior may be more trouble than it's worth, but that's for you to decide.