Is there any work or job experience required for selection in XLRI?

Yes! you can very well get into any of these colleges without work experience. In my batch I had quite a few number of people who had absolutely no work experience. I myself had only 5 months of work experience when I joined.
However, since you lack wok experience, these colleges would evaluate your candidature on the basis of your academics as well as leadership and extracurricular achievements. The NGO work and startup which you have mentioned will definitely be a plus. For SPJIMR particularly, I would suggest that you try to zero in on the specialisation you wish to pursue (You would have to select between marketing and finance since you are a fresher) and try to do some online courses or work which could help justify your interest. For example, you could do an online course in digital marketing or work in the communications department of the NGO you are involved with. Similarly if you wish to opt for finance you could find relevant activities. This should help strengthen your profile.
Hope this helps :)