I agree with Martijn and based on what I see from your examples you should do with this one: **/Immigration/Permanent-Residence/Work-Permit-South-**Africa
In regards to your questions:
Is it worth it? - yes it does
Will google read my parented URL with all the keywords, or only the page's keywords? - Google will take into higher consideration the folder that is closer to your domain name. With your new structure I suspect you would promote the page with the "Immigration" keywords which includes "permanent residence" as one of the many services your "immigration" page includes. Same goes for your work permit. This is how google will see it while at the moment it sees one authoritative page which includes the whole keyword. As Martjin said it really depends in how many pages/services you got.
What should I expect to see from google? - I have witness slight improvement in rankings (+2-3 positions) after I Implemented url re-structuring and schema but I have mainly worked in property related web sites so not sure if this an exception or rule. Someone with an e-commerce web site (where there url structure is a must) could give us his insights in terms of improvements as in every single e-commerce site I have worked, I always made sure the url was structured properly from scratch so I do not have an insight in terms of "improving" rankings.
Will my SERPs be all messed up? - Not messed up but you might end up with lots of 404. Make sure you set redirects from the old URLs to the new Ones. Again it depends the web site. From my experience I changed 4 in the past and only one popped loads of 404s but that was mainly due to a plug in that was displaying search results based on unique criteria, something I could not control.
Hope this helps!

and not the links mentioned above. I see only good in removing these links.