To make use of org-mode but use the familiar vim keybindings, I just use emacs with evil-mode, the vim emulation mode. It works great. I've searched for a vim-centered alternative to org-mode for a long time; this is the best way I've found.

I've used https://github.com/jceb/vim-orgmode for a while now for managing documentation written with org-mode. It gets the job done, but if my project's docs weren't written in org-mode already, I'd just use markdown.

vimoutliner (https://github.com/vimoutliner/vimoutliner) is also terribly mature and appropriate for a lot of tasks one might use Org mode for - certainly worth a look.