In Nintex for SP2016, we have several web service methods available in the endpoint "/_vti_bin/NintexWorkflow/Workflow.asmx". The complete list of method for Nintex Workflow for SP2013/2016 can be found at https://community.nintex.com/community/build-your-own/blog/2017/01/07/nintex-workflow-web-service-me...
Is there any replacement for this on Nintex for O365?
I haven't been able to find anything like it yet. Here's how I understand it so far. Their workflows are powered by the rules of the Workflow Manager in O365 and no longer third party web services can be used. This is why you don't get their Task engine, workflow insight or visual progress.
Now I'm back to using SharePoint REST calls to interact with OTB Workflow Tasks.