For the first video, only basic MATLAB is needed for wavread() and sound() and the flanging code. The Signal Processing toolbox is needed for the frequency response plots whose output is shown but the commands for which are not shown.
For the second video, mostly basic MATLAB is used, but a couple of the routines use some calls from Signal Processing Toolbox. The code also accidentally makes one call to padarray() which is from the Image Processing Toolbox, but that line could be rewritten with small effort.
Neither of those videos require the Audio Systems toolbox. However, if you want to do any streaming (real-time) audio effects, then Audio Systems Toolbox is recommended.