Replace [^a-zA-Z0-9 -] with an empty string.

Regex rgx = new Regex("[^a-zA-Z0-9 -]");
str = rgx.Replace(str, "");

Be aware, that \W leaves the underscore. A short equivalent for [^a-zA-Z0-9] would be [\W_]

text.replace(/[\W_]+/g," ");

\W is the negation of shorthand \w for [A-Za-z0-9_] word characters (including the underscore)

Example at regex101.com

Regex to the rescue!

import re

s = re.sub('[^0-9a-zA-Z]+', '*', s)

Example:

>>> re.sub('[^0-9a-zA-Z]+', '*', 'h^&ell`.,|o w]{+orld')
'h*ell*o*w*orld'

The [..] form is known as a collection (:h /[]) and can contain a sequence of characters and/or one or more ranges of characters, separated with -. It will match any single character that is contained in the sequence/range(s). You can, of course, also match the inverse with ^.

In :h white-space you'll find a collection equivalent to \w:

\w  word character:         [0-9A-Za-z_]

So one approach is to invert/negate that equivalent:

[^0-9A-Za-z_]

Alternatively, collections can also contain the "character classes" found under :h E944. These are the same character classes that have been around forever in the BRE/ERE patterns used by legacy tools and POSIX environments.

Alphanumeric chars have the following character class equivalent:

[:alnum:]   isalnum ASCII letters and digits

You can invert/negate that like so:

[^[:alnum:]]

(You could also probably use negative lookarounds with \w but that's relatively difficult compared to this straightforward analog to [^\w].)

Update: I just realized I didn't address the full pattern you posted. Just look for a character class that's equivalent to \s and you'll find [:space:]. And " is just ". So [^\w\s"] becomes:

[^[:alnum:][:space:]"]

One other thing, this is likely to be the most performant of any possible solutions since others have lookarounds or alternations (|) and those are expensive.

I would use the following Regular Expression: '[^a-zA-Z0-9]'

Pattern nonAlphanumeric = Pattern.compile('[^a-zA-Z0-9]');
Matcher matcher = nonAlphanumeric.matcher('Sales - Actual Results (TY)');
system.debug(matcher.replaceAll('')); // output: SalesActualResultsTY

Demo

This is actually fairly straightforward.

Assuming str is the string you're cleaning up:

str = str.replace(/[^a-z0-9+]+/gi, '+');

The ^ means "anything not in this list of characters". The + after the [...] group means "one or more". /gi means "replace all of these that you find, without regard to case".

So any stretch of characters that are not letters, numbers, or '+' will be converted into a single '+'.

To remove parenthesized substrings (as requested in the comments), do this replacement first:

str = str.replace(/\(.+?\)/g, '');

function replacer() {

  var str = document.getElementById('before').value.
    replace(/\(.+?\)/g, '').
    replace(/[^a-z0-9+]+/gi, '+');

  document.getElementById('after').value = str;
}

document.getElementById('replacem').onclick = replacer;

<p>Before:
  <input id="before" value="Durarara!!x2 Ten" />
</p>

<p>
  <input type="button" value="replace" id="replacem" />
</p>

<p>After:
  <input id="after" value="" readonly />
</p>