redirect based on host and uri

I believe you can actually get what you need from the first iRule, but simply invert the cases, as in:

when HTTP_REQUEST {  
    if { [HTTP::uri] eq "/" } {
        HTTP::redirect "https://newsite.com/identitymanagement/default.aspx"    
    } elseif { [string tolower [HTTP::host]] eq "oldsite.com" } {
        HTTP::redirect "https://newsite.com[HTTP::uri]"
    }
}

That way, if the request is "http[s]://oldsite.com/" or "http[s]://newsite.com/", the redirect will be to "https://newsite.com/identitymanagement/default.aspx". Otherwise, a redirect occurs if and only if the Host header is "oldsite.com". (Notice that I removed the

string tolower

HTTP::uri

Instead of using an iRule, however, you should consider employing Local Traffic Policies if you are using 11.4 or above, or HTTP Classes if you are using a version lower than that:

• SOL15085: Overview of the Local Traffic Policies feature
• SOL7280: Overview of the HTTP Class profile

Generally, these mechanisms are more efficient than an iRule.