If you are on a corporate computer and do not have permissions to install MSI files, you may try the following procedure. I wan't call it "portable" as it is does have some dependencies which it might not be possible to circumvent but it depends on the strictness of your configuration.
Download the installation files from the following link and extract the compressed folder (ZIP) to the following folder:
Files for Outlook 2007
Files for Outlook 2010/2013
Target folder on your machine:
You may copy the files to a different folder, but then you also have to edit GogTasks-inst.reg
Among the downloaded files you will find a file named GogTasks-inst.reg. Attempt to import that file to the registry by double clicking on it and confirming permissions to the popups you will face. You may have to run it as administrator (right click -> Run as administrator).
If your policy does not allow to automatically import registry files, you may attempt to run regedit manually and manually enter the information from the .reg file. Open the .reg-file in notepad and create keys in the folders specified with the data you see in notepad.
If neither of these methods work, then you will not be able to run GogTasks