No, my work experiences are not continuous. I thought when they say you can work in different jobs it means it does not need to be continuous. And for CEC that seems not to have the continuous job requirement, I can not count those part time paid jobs during my PhD.. Such a terrible program. Canadian immigration system is the perfect example of nonsense. Someone like me after over 6 years in Canada with a PhD, job and high IELTS score can not still enter in to the EE.
You must have at least one year of continuous full-time work experience in a single and an eligible NOC (your primary NOC). Once you meet this requirement, you can add up all other work experiences even though they are not continuous (provided they are in an eligible NOC).
For instance :
You worked in Job A from 01-2013 to 11-2013 ~ 10 months experience
You worked in Job B from 01-2014 to 01-2015 ~ 12 months experience
===> You should set the NOC of this job as your primary NOC.
You worked in Job C from 02-2015 to 09-2015 ~ 7 months experience
Since you have met the minimum requirement because of Job B, you can then add up the experience gained in remaining jobs (12+10+7 = 29 months). In this case, you can claim points for 2 years of work experience.
You get maximum CRS points for 3 years of foreign work experience. Any work experience after that is superfluous for the purpose of your CRS score.
I think the mistake you are making when creating your EE profile is you are setting your primary NOC incorrectly. Like shown above, the primary NOC you choose MUST belong to a job that you've been in for at least 12 months continuously AND it should fall under NOC categories 0, A or B. I had a friend do the same mistake over and over again until I figured out what she was doing wrong.
As for your Canadian work experience, it should have been recent (within the past 3 years, I believe) and any work experience gained while you were a full-time student in Canada doesn't count.
The system isn't perfect but it isn't a "perfect example of nonsense" either. This is a points based system and there are flaws for sure. Several of my friends were not able to make the cut because of the (over) emphasis on language test bands. CLB-9 is near-native level fluency in English - I believe CLB-7 to 8 would be more than enough to live in this country, yet, the system is such that an applicant loses a LOT of points for being in one band below CLB-9. (To give you an idea, if you had a Master's degree with 3 years of foreign work experience and age < 30, you'll have ~ 470-480 points with CLB-9. With a CLB-8, your CRS will be around 440 - 445.) It is what it is, I guess.
Hopefully, you get to submit a successful profile and get your Canadian permanent residence.
Good luck!