First, open > About this Mac > Storage, so you can see what is taking up space of the hard disk.
You can delete all your DMGs if they are stored on your user folder. DMGs are often installation packages, so you can delete them without any problem. Also, if you aren't using old applications, you can uninstall them without any problem. Most of the apps are uninstalled just dragging them to the Trash, but some applications need an uninstaller to be uninstalled.
To install Office 2011 if you are running an older Office version, you can install Office 2011 without having an old Office version installed on your Mac. There aren't upgrade versions for Office for Mac > http://www.microsoft.com/mac
Your Mac stores the downloaded updates on a system folder, and you can delete them if you need space. However, if your hard disk gets more free space deleting other things, better.
On OS X, most of the apps just run being dragged to a folder, and you can use those applications without any problem. However, other apps (as Office) needs other files on your OS X volume, so you may have problems running it from an external disk. If you have enough space on the internal disk, run your applications from there