It requires passion, interest and commitment for one to start, complete and earn a certificate at any online course. This is also being well acknowledged by recruiters these days.
I hope you have taken the online courses for shaping a specific part of your career or advancing into a particular domain. So, phrases like "self-taught ___" would help the recruiter recognize the work you put in.
Example: If you have taken online courses for becoming a data scientist, then including a phrase like "A self-taught data scientist" would help the recruiter learn that you have self learnt your skills.
I had and have it on my resume and LinkedIn profile, and it worked really well, in fact I was well appreciated by the interviewers for putting those extra efforts. After all those days of HW's, assignments and quizzes, it feels good.
Coming to the resume, including courses would just extend it's length without adding much value. Instead, include a project which you have done as part of the MOOC, and then include this line: "Done as a part of the ___ MITx1003 course on EdX".
This would help the resume stand out, and also earn brownie points, as you have not only finished the course, but also have done a project with the knowledge obtained.
Same can be done on LinkedIn profile too. Here, you might want to increase the length of your project description by adding the University and the Professor's name, topics learnt during the course, etc. Include the course certificates in the certifications section.
Make sure your recruiter knows that you have put in those extra efforts to learn those courses, apart from classroom education. Resonate the same, in the summary section of your LinkedIn profile (Feel free to refer to my profile if you need help).
A similar answer which I have written (but is a bit inclined towards stats)
A Quora link which can help you in adding the MOOC details and certifications to your LinkedIn profile.