Search and replace
 

I wish to reduce my use of Microsfot Word and OmniOutline shows some potential. One thing though that I like very much on Word is the auto-correction. I'm willing to live with it if I can use a Search and Replace in Omni Outliner. For instance, is there such a thing or a trick or even an AppleScript that I could use to replace my abbreviation with complete names?

Either get Textpander which is currently free or TypeIt4Me (which preceeded Word's autocorrect by a long way in the Classic Mac OS days). These provide system wide auto-completion. Textpander even has the ability to auto-input images for you (e.g. a scanned signature) and formatted text rather than plain text.

simpler still: type command-F
brings up find window with find text box, replace text box and a "Replace All" button (among others).

Or am I missing something?

Yes. Command-F can't replace e.g. addr with your full address correctly formatted, aligned and spread over several lines like an auto-complete utility can. Also, having og get auto-expanded to OmniGraffle in a browser text input box like this is not at all easy to do with command-F.