Any way to shorten this switch case iRule?

I believe that the data group answer is the best one if you are in fact not performing globbing. Here is how I would do it (though not tested!):

tmsh create ltm data-group internal redirector-base type string { records add { \
    "/file1.html" { data "http://www.newdomain.com/en-US/destination1" } \
    "/dir1" { data "http://www.newdomain.com/en-US/destination2" } \
    "/dir1/" { data "http://www.newdomain.com/en-US/destination2" } \
    ... etc ...
    } }

(You could -- and probably should -- do this with an imported external data-group, but I use an internal group for illustration).

Then the rule:

when HTTP_REQUEST {
    set base [class lookup "[HTTP::path]" redirector-base]
    
    if { $base ne "" } {
         Extract URL parameters
        set urlPath "[string tolower [HTTP::path]]?"
        if {[string tolower [HTTP::uri]] contains "?"} {
            set newUri [string map -nocase [list $urlPath "?"] [HTTP::uri]]
        }
        else {
            set newUri ""
        }

        HTTP::respond 301 Location "$base$newURI" 
    }
}

Note a few things:

1. This will not work if you need to employ globbing (though, strictly speaking, you could iterate through a list of glob matchers that are keys in a data-group, but that may be [considerably] less efficient than the switch);
2. I moved the

   $newURI

   computation inside of the conditional. If there is no match, there's no point in performing the calculation;
3. You use a pattern that I very commonly see, namely:

   [string tolower [HTTP::path]]

   . While it is true that some filesystems are case-insensitive, RFC 2616 states that everything but the scheme (i.e., the leading 'http' in this case) and the hostname should be treated in a case-sensitive manner. See RFC 2616 3.2.3 [1]. As a practical matter, "flattening" the case of the path costs CPU cycles and I believe it to be of no practical value, especially if users are not typically typing in the uri-path part, but rather they are getting to these locations via hyperlinks.

[1] Specifically:

   When comparing two URIs to decide if they match or not, a client
   SHOULD use a case-sensitive octet-by-octet comparison of the entire
   URIs, with these exceptions:
      - A port that is empty or not given is equivalent to the default
        port for that URI-reference;
      - Comparisons of host names MUST be case-insensitive;
      - Comparisons of scheme names MUST be case-insensitive;
      - An empty abs_path is equivalent to an abs_path of "/".