NeoOffice is not a suite. Its application bundle is presented to the user as a single icon. The bundle contains a small number of executables and a plethora of dynamic link libraries or .dylib files. There are two ways to access the various modes of NeoOffice. One is to open (double-click) on a document created using the mode you want. The other is to use the NeoOffice menu within the application to switch to the mode that you want.
Not exactly shortcuts, but if what you are trying to do is to jump directly to a new Spreadsheet or Text document or Presentation or open a recent file you've been working on, this little app Nomu might help you. It installs an icon in your menu bar...