sedulous (formal) showing great care and effort in your work
assiduous (formal) working very hard and taking great care that everything is done as well as it can be synonym: diligent
diligent (formal) showing care and effort in your work or duties
These definitions look alike. What they have in common is that these words mean to take care and to put effort into your work.
All words are formal. None of these seems to be a proper term in a specific field, e.g. medical, law.
I also looked at Merriam-Webster to get more details. This adds the connotation of steady and earnest to diligent and unremitting attention and persistent application to assiduous. But in the end, these additional information are again describing an equal thing, i.e., continuously doing your work. The entry on sedulous doesn't add any more content; it refers to diligent and again describes the word with perseverance.
From this point (checking dictionaries only), I don't see any difference at all. I continued with a corpora search.
Diligent is most used in combination with work, effort, research, study but also student, people.
She's a diligent student.
His diligent research identified the value of ...
Assiduous is also most used with work, effort, research but not with student, people. Merriam-Webster's Learner's Dictionary entry on assiduous lists student as example though.
He's assiduous in his work.
With assiduous attention to detail ...
Sedulous is most used, um, to little results. BNC has even less content. Merriam-Webster's example is, once again, a student.
So, diligent is used most often, followed by assiduous and sedulous is quite rare.
All words are formal. All words seem to be usable as an attribute to a person (e.g., student) but also specifying the intense care and effort on work, e.g., a research.
I don't see any significant difference in these words, besides frequency. When is a student diligent, assiduous or sedulous? And when is a research diligent, assiduous or sedulous? Or simply: What are the subtle distinctions which aren't represented by dictionaries?