How to escape special characters in PowerShell?

You're using Invoke-Expression to call an external program:

• There's no reason to do that, and Invoke-Expression should generally be avoided: it causes quoting headaches (as in your case), but, more importantly, it can be a security risk and there are typically better solutions.

  • As an aside: Unfortunately, even with direct invocation there can be quoting challenges around empty-string arguments and arguments with embedded " chars. - see footnote [1] and this answer.

• If you instead invoke the external program directly - as any shell, including PowerShell is designed to do - your problem will likely go away:^[1]

& <path_to_exe> -install $user $password

Note: &, PowerShell's call operator, is only needed if your executable's path is quoted (e.g, "C:\Program Files\foo.exe") and/or is specified via a variable reference (e.g., $HOME\foo.exe); otherwise, you can invoke the executable as-is (e.g., to invoke cmd.exe, use something like
cmd /c 'echo hi').

Separately, if you do ever find yourself needing to escape any of the characters in a set of characters, use -replace with a character class, [...]:

Note: This is not necessary for passing arguments, neither to external programs, as shown above, nor to PowerShell commands; however, due to PowerShell's broken handling of " characters embedded in argument values passed to external programs, you may have to escape " characters (only), as \"^[1].

PS> 'a*b\c~d;e(f%g?h.i:j@k/l' -replace '[*\\~;(%?.:@/]', '`$&'
a`*b`\c`~d`;e`(f`%g`?h`.i`:j`@k`/l  # all chars. inside [...] were `-escaped

^{Note: Since \ has special meaning even inside a character class, it had to be escaped as \\ - all other chars. are used as-is.}

For more information about the -replace operator, see this answer.

^{[1] There is one character that still causes problems: embedded ". For historical reasons, PowerShell does not properly pass embedded " correctly to external programs, and annoyingly requires manual \-escaping - see this GitHub issue for details. Applied to your solution:& <path_to_exe> -install $user ($password -replace '"', '\"')}

Using the below will escape the characters using the escape prefix you mentioned. The normal escape prefix is \ as shown below. I have set it this way so it is easier for you to add additional characters to escape or change the escape prefix.

function Set-EscapeCharacters {
    Param(
        [parameter(Mandatory = $true, Position = 0)]
        [String]
        $string
    )
    $string = $string -replace '\*', '`*'
    $string = $string -replace '\\', '`\'
    $string = $string -replace '\~', '`~'
    $string = $string -replace '\;', '`;'
    $string = $string -replace '\(', '`('
    $string = $string -replace '\%', '`%'
    $string = $string -replace '\?', '`?'
    $string = $string -replace '\.', '`.'
    $string = $string -replace '\:', '`:'
    $string = $string -replace '\@', '`@'
    $string = $string -replace '\/', '`/'
    $string
}

$Password = Set-EscapeCharacters $Password