Trying to map <Ctrl>+<hjkl> to <Left Down Up Right> globally (Vim-like arrow keys) with xmodmap

Solution 1:

It is surely very strange idea to turn Ubuntu into the codename "VimOS". I think much more adequate to map Vim's keys to some free and equable more cluster of the keyboard. Or definitely NOT due to it is also might be useful.

However I do not deletes my first suggest about Vim mappings and should to say that answer to your question exist here:
System wide vim-style (hjkl) navigation

Partially I agree this view (thanks to shell hell):

_{NOTE 3: Setting up Ctrl / Meta + H,J,K,L keybindings seems to be simplest way to have vim-style navigation but it’s not. First: you would have to do this on per application basis which is tiresome process. Second: you’ll probably end up breaking default mappings for any given application. Last but not least: some apps e.g. rtorrent or htop don’t let you change their defaults, save by patching their sourcecode. For similar reasons you won’t get job done with Super / Hyper, either.}

And also I found near answer here:
Superuser: Mapping Super+hjkl to arrow keys under X

Vim uses a switching modes to mapping keys. So xmodmap for Vim it is some pluggable globals what breaks classic Vim experience. Even so to claim it sounds pathetic _;)

Vim supports several editing modes - normal, insert, replace, visual, select, command-line and operator-pending. You can map a key to work in all or some of these modes.

Mapping keys in Vim - Tutorial (Part 1)
Mapping keys in Vim - Tutorial (Part 2)
Mapping keys in Vim - Tutorial (Part 3)

Solution 2:

I have Tux-J and Tux-K mapped to Up and Down in KDE, it is relevant for all applications. It is actually rather easy to configure.

1. Go here: System Settings -> Custom Shorcuts -> Preset Actions
2. Now right-click Preset Actions and choose New -> Global Shortcut -> Send Keyboard Input
3. Call the new shortcut VIM-J
4. In the Trigger tab click the Shortcut button and them press Tux-J.
5. In the Action tab enter Down
6. At the bottom of the window click Apply.
7. Check that the shortcut works. If so, then configure the remaining HK and L keys.

Enjoy!