OK, i'm not too sure whats going on there, but it sounds like your putting the addons onto the CD, instead of the hardrive.
Make sure you've done the following:
1. Get Winrar/Winzip (incase you already havn't)
2. When downloading, save to somewhere easy like the desktop (you can delete/move the rars/zips later.)
3. Open your zip file. Inside should be some .pbo files, and sometimes a readme etc.
4. Open your OFP addons directory. This should be something like 'C:/Program Files/Codemasters/OperationFlashpoint/Addons.' There will already be some /pbo files in here.
5. Click and drag the .pbo files from that zip file into this folder.
6. That should work.
Is there a particular addon your having trouble with, is it with all addons?