minor irule change, but its my first one. go easy on me.

May I suggest using something like below. Since you are trying to match based on the start of the uri, use HTTP::uri. Also, looks like the start of your uri's are the application roots, so if you match with glob(_) adding the second "/" will ensure you get the expected behavior. But, yes in theory /erma2* and /erma3* should match before getting to your /erma* switch.

when HTTP_REQUEST {
     Check the requested path with wildcard matching
    switch -glob [HTTP::uri] {
        "/rradmin/*" {
             /rradmin URI
            log local0. "[IP::remote_addr]: Request for /rradmin sent to pool pool_rradmin_ecms.gov_new_443"
            pool pool_rradmin_ecms.epa.gov_443
        }
        "/erma2/*" {
             /erma2 URI
            log local0. "[IP::remote_addr]: Request for /erma2 sent to pool pool_erma2_ecms.epa.gov_new_443"
            pool pool_erma2_ecms.epa.gov_443
        }
        "/erma3/*" {
             /erma3 URI
            log local0. "[IP::remote_addr]: Request for /erma3 sent to pool pool_erma3_ecms.epa.gov_new_443"
            pool pool_erma3_ecms.epa.gov_443
        }
        "/erma/*" {
             /erma URI
            log local0. "[IP::remote_addr]: Request for /erma sent to pool pool_erma_ecms.epa.gov_new_443"
            pool pool_erma_ecms.epa.gov_443
        }
        default {
             everything else
            URI log local0. "[IP::remote_addr]: Default ecms.epa.gov sent to pool_default_ecms.epa.gov_new_443"
            pool pool_default_ecms.epa.gov_443
        }
    }
}