I'm also a OneNote fan. I use it in a similar fashion - tons of work-related stuff, a bunch of personal stuff, and a notebook shared with my SO so we can both update grocery lists, etc.

I've got the OneNote app on my iPhone and it works well enough for what I need to access on the go. What trouble do you have accessing it when you're not at home? My biggest use-case for OneNote on the iPhone is to tick items on the grocery list - it works great and changes propagate to my SO's phone in under a second.