Hi,
jammiii did some Picasa 3 portable but it cannot save your setting about pictures and albums as well.
I create this application.
You have to extract somewhere files and copy binaries to App\Picasa3
Please use this with PortableFileAssociator https://portableapps.com/node/15583
You can use this application across more computers 
Here is link http://rapidshare.com/files/224702800/Picasa3Portable.zip.html
It is my first published work. Don't yell on me ;o)
Any feedback is welcome.
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I'm pretty sure jammiii was planning on updating his own soon, so unless you had permission from him to do this I think this is a little rude.
It can be rude but almost 3 months is not soon.
Sorry
Portable application without saving setting is not portable.
Sorry again.
Filip,
Thank you for your work. I do not believe it was rude to provide a working solution. But, the download link had a limit of 10 which is already exceeded. Can you post another link or update the fileshare account? Please continue your contributions and do not become discouraged. The more people sharing the better for all.
Can you upload it again?