When I find myself wanting to deal with structured text in multi-line chunks, I usually find the $/ variable to be helpful ( look for $INPUT_RECORD_SEPARATOR in perlvar). If you can come up with a text string that defines the boundaries between the chunks, you can read them in and deal with them individually. With a small file, you could slurp in the whole thing and split it with a regex, but that runs into trouble with larger files.

So, something like this will give you your IPs and their interface names as a hash:

#!/usr/bin/env perl
use 5.010; use strict; use warnings;
use Data::Printer;

my %ints;

local $/ = "next\n    edit"; # break lines on this instead of newline
while(my $chunk = <DATA>){
  if( $chunk =~ /"(\w+)".*set ip (\d+\.\d+\.\d+\.\d+) /s ){
    $ints{$1} = $2;
  }
}

say p %ints;

__DATA__
config system interface
    edit "dmz"
        set vdom "root"
        set ip 192.18.254.1 255.255.254.0
        set allowaccess ping fgfm
        set type physical
        set alias "Guest-Wlan"
    next
    edit "wan2"
        set vdom "test"
        set ip 10.4.254.198 255.255.255.252
        set allowaccess ping https ssh snmp
        set type physical
        set alias "To MON ospf int"
    next
    edit "wan1"
        set vdom "root"
        set ip 1.1.1.1 255.255.255.252
        set allowaccess ping https
        set type physical
        set alias "To Internet"
    next
    edit "modem"
        set vdom "root"
        set mode pppoe
        set allowaccess fgfm
        set type physical
    next
    edit "ssl.root"
        set vdom "root"
        set type tunnel
    next
    edit "ssl.MyRealm"
        set vdom "MyRealm"
        set type tunnel
    next
    edit "internal1"
        set vdom "root"
        set ip 10.1.16.3 255.255.255.0
        set allowaccess ping https ssh snmp fgfm
        set type physical
        set alias "To MON Internal "
    next
    edit "internal2"
        set vdom "MyRealm"
        set dhcp-relay-service enable
        set dhcp-relay-ip "192.168.1.1"
        set ip 192.168.2.1 255.255.254.0
        set allowaccess ping https ssh snmp fgfm
        set type physical
        set alias "To MINE"
    next
    edit "VPN-Dial"
        set vdom "root"
        set type tunnel
        set interface "wan1"
    next
end
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