Hello.
Disclaimer: I run PortableApps from HDD on all my computers and sync it with Dropbox. I do that because I like to have the apps with their settings in one, easily transferable folder. I do not carry it on a stick. So, if you're anything like me keep on reading. 
Problem: If you try to integrate the portable 7-zip with the shell context menu it'll throw the "Can't find 7-zip.dll" error message at you.
Solution:
1. Install a "normal" version of 7-zip from their site: http://www.7-zip.org/
2. Grab 7-zip.dll from the installation directory and stick it into your "PortableApps\7-ZipPortable\App\7-Zip\" folder
3. Uninstall the "normal" version of 7-zip
4. Now you can enable and configure the shell context menu integration
Remember: This is not in the true spirit of portability. If you do that it'll leave traces on the computer so use it only with your "persistent" PortableApps installation.
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You shouldn't do this. It removes all traces of portability from it - it won't keep its settings in the portable location.
I am a Christian and a developer and moderator here.
“A soft answer turns away wrath, but a harsh word stirs up anger.” – Proverbs 15:1
Yes, I'm perfectly aware of that... that's why I wrote about it in my post... It seems you didn't read it at all... :/
I did read it all, but you've just said "leaves traces" and that it "should only be used with a persistent PortableApps installation". What I'm saying is that it doesn't just leave traces - it is not portable in the slightest. It's just the same as having 7-Zip installed locally.
I am a Christian and a developer and moderator here.
“A soft answer turns away wrath, but a harsh word stirs up anger.” – Proverbs 15:1
i tested this this weekend and i found that they do not work the same as when they are installed onto a flash drive or other removeable media.