I am a software developer considering a post-graduate diploma in Canada. My question is:

Can I do freelance software consulting work for Canadian and foreign clients:

1) while on a student visa?

2) on an Off-Campus work permit while studying?

3) on the Post-Graduation work permit that I get after my studies. (freelancing fulltime)

If so, can this freelance work be shown as work experience on my PR application?

A study permit is not a work permit, it does not in itself permit work in Canada. However, in many cases, subject to province and institution, study permit holders are granted permission to work on and/or off-campus under certain circumstances. Otherwise an open work permit (or exemption from the need for a work permit) does allow for freelance work so long as it does not contravene any specific exclusions stated on such a permit.

Freelance work can otherwise be counted on a PR application so long as it is adequately documented.