You can with some things, but I wouldn't recommend it. When you install software on windows key entries get stored in the registry hive. When you bring an external drive to another computer and open your software it looks in the registry and if it cannot find it you'll most likely will get problems. Along with that issue installers also install files to other directories besides program files. The directories I can think of are
%programdata%
%appdata%
%temp%
%homedrive%
%allusersprofile%
%systemroot%
try going to those in your explorer address bar or in start/run
There are programs out there like thinapp for example that can self contain those registry entries and directories and let you make portable style apps, but installing a bunch of vst's can be a headache because each plugin can give different results. I would recommend small in file size plugins and better yet simple dll plugins that can exist anywhere you drop it. Then there are also program requirements like .net, vc, java, and a bunch more and if the other computer does not have it then it kind of defeats the purpose of being portable. Its also recommended doing such in a clean installation of windows in a virtual machine.
So not saying that it cannot be done but it will be a project in itself and you need patience with getting it right hence why I wouldn't recommend it.