Paste the current date-time in OmniOutliner While writing in OmniOutliner, I would like to insert the current date or current date-with-time.

Is there such a feature as "Now" in OmniOutliner 5.4.1 for macOS?
From the menu Edit->Insert Time Stamp - and you get a set of options.

Some of those have short cut keys e.g.

On a US keyboard

⌘| for Short date and time
⌘⇧| for Long date and time  

Difficult on a UK one as you need shift to get a | so you only get the short date and time.

See the OmniOutliner help. It has a detailed entry for Edit menu