need to check for a path in an irule

Is your code not working for you? I will say that it can be somewhat simplified, since your outside if/else conditionals check the same condition and the inner [if]s are negations of one another:

when HTTP_REQUEST {
    if { [string tolower [HTTP::host]] equals "itservices.ou.edu" } {
        if { [string tolower [HTTP::path]] starts_with "/norman" } {
            HTTP::redirect "https://ouitservices.service-now.com/ess_portal"
        } else {
            HTTP::redirect "http://itscnorman.ou.edu"
        }
    }
}

If you are running at least version 11.4, you should be able to accomplish this with a Local Traffic Policy, as well:

• SOL15085: Overview of the Local Traffic Policies feature

A Local Traffic Policy should, in general, be more performant, and is integrated with the web UI and CLI.