I would love to have essays reviewed both in terms of quality writing and in terms of its content. I have researched a few sites but this service does not seem to exist.
I've never used any online service for reviewing, editing, and/or critique. I always get it from peers and mentors.
There are some advantages to having your writing reviewed online, like speed and convenience, but in the end, you don't really know where it's going or who's really reading it.
I would recommend finding people you trust--coworkers, friends, teachers, professors, family members--to look over it, and to tell them what you want them to look for ahead of time. Also, be sure to ask for critique from people who would be qualified to give it to you. For instance, asking an English major with a specialty in creative writing to review your technical essay on infectious diseases may not be the best choice.
The services exist, google "critique service" (without the quotes). Ignore the "copyedit" services (if that is all they do), they are just checking spelling and grammar and formatting.
Actual critique services are just damn expensive; running roughly $100/hr, or if the work is long enough, around 2-4c per word, OR $10.00/page for short works, or $8.00 per page for long works. I know you are writing essays, but if somebody wrote a 90,000 word novel (typical) that would be 360 pages, and by these prices anywhere from $1800 to $2900 for a critique.
They are easy to find, most will give you a quote on a word count.
An essay of 5000 words or so may not be bad, but still perhaps $200.
If you want your writing evaluated, apply for a relevant university course and use said writing as a part of the work you produce for that course (e.g. a university assignment, a thesis, a research paper, etc).
You may be able to pay an academic thousands of dollars to evaluate your writing and give you feedback, but they're typically very busy people so you'd generally be better off just paying for the university course they're teaching, or getting them to become your PhD or research Master's Degree supervisor instead.
For the last year or so, I've been on a critique-exchange site called "Scribophile". They work on a "karma" system --you typically critique three other people's work for every piece of work you put up for review.
I've found it very useful. There is a strong focus on fiction, but you can also post non-fiction. And it's a good community ,with a wide range of writers, from new beginners, to writers with a long string of publications and established careers. The main commonality is that it's people who are serious about writing, and about getting better at it.
(It's free to join, premium features are available if you upgrade. I have no personal affiliation with the site other than membership.)
Depending on whether you're a student at a university, I would recommend using the Writing Center at your local college campus.
Absent of that option, I would maybe recommend Fiverr.com, namely, the beta readers there. I use Fiverr beta readers to beta read my short stories (creative writing has always been my weakest spot in writing) and they've been pretty helpful; however, you would probably have to do some research as to which beta readers would be most appropriate for the type of writing you're doing. Also, as a shameless plug, I do run a gig on Fiverr.com (https://www.fiverr.com/brianhinman806) that is essentially an off shoot of the services I used to offer as a Writing Consultant for the University of Wyoming. I would be happy to work on your writing. However, all gigs on Fiverr are paid (not free).