Does anyone know how to effectively do pivot tables in Google Docs? Do they work the same was as in Excel?

In Libre Office or Open Office, they are much the same as Excel. I don't know about Google Docs unless that is built upon Libre/Open Office tools. FWIW, Libre Office much more compatible with MS Office applications than is Open Office. They have expended a huge amount of resources on making the Libre Office tools compatible with MS Office.

Neither of those are SaaS products though, right?

No. Libre and Open Office are installable applications. I am not sure if Libre Office has a web-based version or not. You can find out all about it at www.libreoffice.org.
There is a portable version that will run on your iAnything, Android devices, etc. Find it here: http://www.libreoffice.org/download/portable-versions/