Is there a polite way of telling my internship adviser?

Well if you’re 40 they’re around 65-70 so I’d say another 15 years.

Seriously, PhD in Math and no job? That’s either a tragedy or performance art. Go work for a non-profit on whatever the hell journalism topic you were hoping to write abut and blog your heart out about it.

I am very ambivalent – perhaps pretending to work for my advisor for $350/month and food and good living space and all the bills is not a bad job after all.

I will work on social issues non – profit after I get better medication for my depression.

IANAL, but my understanding is that unpaid internships are only legal if there is some educational benefit involved. If you live in the US, I would suggest going to your local state offices and check out the law. Your “employer” might owe you a lot of back wages.
Are you learning anything in this slave job? Why do your parents support it, unless they have issues and don’t want to let you grow up.
Unless you have a number phobia, I’m sure you can find some jobs with some degree of math knowledge but nothing like what you learned in a PhD program. Statistics, maybe? And forget journalism - you might as well as go into buggy whip making.

However finding a job is not going to be easy, not a real one. I’d reject a resume with an unpaid three year internship right away. I’d rather see one with three years of unemployment.

Usually when someone is in a bad job situation the advice is to find a new one to avoid financial problems. But unless your parents are going to cut you off for looking for paid employment, that isn’t your problem, is it? Check out the law, ask for money to continue, and if they kick you out report them and sue for back wages. Find a pro bono attorney at a law clinic to help. And of course look for a job - in fact look while you are supposedly working, it is not like you owe these people anything.

And, I almost never say this, but you might benefit from some therapy to find out why you hate what you must be good in and why you’ve allowed this situation to go on for so long. It might be very helpful.

Is this some kind of post doc?
BTW, I was in grad school in the late 1970s - and I made more than $350 a month back then, not inflation adjusted.

What particular area is your PhD in? (Like, what did you do your dissertation on?) And what kind of work does your internship involve? I’ve never heard of a PhD in math having an internship; but then, I don’t get around much.

If it did, there’d be a lot of cat journalists out there.

How were you 38 last year and “over 40” now? Does your PhD in math come with the power of aging you more rapidly than the rest of the world?

Came with a 50% pay cut, too.

Where can I find professional help on that matter?

He is using a logarithmic scale.

On making your resume presentable? I’d start searching on-line for resume advice. I know there are resume writing agencies, but my impression is that lot;s of them are ripoffs.

I know what my friend Nick the headhunter would say. You need to list your strengths (not YouTube videos) and look at them from the perspective of making money for an employer. Then you’ve got to research companies that might make use of your strengths. If any of these have people with advanced degrees like yours, read their papers. Then send the authors email about their papers, asking questions, (I assure you, no one does this.) I don’t know what branch of math you did research in, but there are tons of jobs in data analytics these days and not that many people with the expertise to really do them.
Anyhow, if you hit it off with any of these people, you can ask them about work, and eventually ask if there are any openings. Why this convoluted path? Because you are going to need a champion inside the company. Someone who says that he knows your work record is spotty, but you seem like someone who understands the field and is interested. No guarantees, but submitting your resume even for a specific job isn’t going to work.

I’d also recommend professional society meetings, local branches. Cheap or free in most cases. I know you don’t like math, but I bet you can find something you do like in the general field, and the alternative is flipping burgers.
Your big advantage - PhDs in math get a bye on eccentricity in many cases.
Resumes are only good for getting sorted, either automatically or manually, and for giving an interviewer who knows nothing about you something to ask questions about. The best job searches don’t even require them. It is a lot more work than submitting resumes to job sites and company job pages, but the chances of success are much greater. Especially for you.
If you want to do something else, then do it. My wife became a writer by starting with a review of toys for the local paper, working up to stories for the Princeton version of the Chicago Reader, and finally to books.
BTW, if your internship is remotely academic, write a damn paper or two.

Are you, by chance, somewhere on the autism spectrum?

Yes, he’s autistic, but he’s also dependent on his parents in an unhealthy way and says this is because his family is “Jewish intelligentsia.” Search for previous threads he’s started to hear more about his story. He’s been given all sorts of good advice here, none of which he seems to take.