Deleting applications and everything that has to do with them?

Preferences are usually stored in ~/Library/Preferences (the tilde means "home folder"). You can just paste this path in the "Go to folder dialog" in the Finder.

CT's answer is not wrong; that is where such things are usually stored, but different programs have different ways of storing user-specific files.

There are other locations for Audacity and VLC. Look specifically for these files and folders:

~/Library/Preferences/VLC/

~/Library/Preferences/org.videolan.vlc.plist

Audacity may have a .plist stored at that same path. It also creates a folder in Application Support:

~/Library/Application Support/audacity

If you installed those programs for "all users" look for them in the same locations at the root level of your startup volume, e.g.

/Library/Preferences/VLC/

/Library/Preferences/org.videolan.vlc.plist

/Library/Application Support/audacity

What you said to be there is not there.

Look for them in the locations I specified.

You are looking in the main "all users" Library, not your own. As you can see from my screenshot, they are both in the user Preferences folder:

The user Library is hidden as of Mountain Lion, but you can show it in Mavericks.

Temporarily: Hold down the Option key and select Library from the Go Menu.

Or, as CT already pointed out, Use Go to Folder from the Go menu and paste in this path: ~/Library

Permanent: Show the View Options for the Home folder (Finder, Select Home, View Menu, Show View Options) and check the box to Show Library Folder

Nearly every application stores its preference file in <user>/Library/Preferences.

Applications might also store some configuration files in <user>/Library/Application Support, inside a folder named after them.

Some not-so-well-behaved apps may have their own folder in <user>/Library.

In your original post, you say that you have deleted and then redownloaded "enough" apps, and that the reasons for doing so are not important.

I have to say I'm intrigued. At the worst case, you might need to restore the apps from your backup. Once. But I can't see a useful or optimal reason for doing this. Perhaps there may be an easier way to achieve your ultimate goal?

Malware does not usually reside "inside" another app, unless the app has been specifically modified for that purpose. If you downloaded illegal copies of software from some dubious website, then that is a possibility. (But downloading it again from there will only restore the malware.)

Did you have reason to think you might have malware? Malware on OS X does exist, but it's rare.

All User preferences are stored in the User Library, yes. Your computer has a Library folder at the top level of the hard drive, and system-wide settings that apply to all users are stored there (e.g. network connections).

Apple recently made the user Library hidden by default: their thinking is likely that if you don't know how to access or reveal a hidden folder, you've probably got no reason to go there. 😁

If you want to unhide the user Library folder and have a browse around, then by all means do so. However, I would advise caution before deleting stuff, particularly Apple stuff.

There are many webpages detailing the many ways you can unhide the folder. Barney above has outlined one.

that was my alias wrote:

I was being precocious; deliting apps just in case they had any malware inside them. You know, the kind of thing a computer illiterate person would do. Or maybe I was right in doing so. So, all preferences are stored under <user>?

Also, the fact my personal library is hidden... not sure if I like that.

User preferences are stored in the user library, you are looking in the wrong library.

The user Library is hidden for good reason, some people can not tell what is what and should not enter it, especially when deleting things

Many 3rd party apps come with uninstallers, (VLC for example), it's best to use them to uninstall.

Mac OS X

Drag the VLC application to your trash can. You can also remove the configuration file and the cache files in ~/Library/Preferences/VLC/. There is an AppleScript on the disk-image which lets you do this automatically.

If that did not work, you can double-click on the Applications icon. This will bring up a list of all applications on your Mac. Scroll through the list of Applications, then press and hold the Ctrl button to bring up a table of options and actions. Click on "move to trash".

that was my alias wrote:

That is really helpful. Before I grant the "solved my question" award to you, could you explain what all those filenames mean? I am talking about the filenames of stored preferences. I would like to know how to tell those apart to know which ones to delete.

Most will follow a "backwards URL" model, thus: com.company.software.plist.

Others will be named more prosaically or deliberately obscurely.

However, it's worth pointing out that there is little point in spending time combing through these files. Most are very small - 4Kb or so. If you've deleted the app, then they will never be used, never be read, never cause a problem.

If you want to delete the preferences of an app because you think the prefs may be corrupt, then that is a very occasional task performed on one file, rarely.

The best way to know whether you should delete a file: if you don't know what it does, leave it alone.